diff --git a/src/cmd/go/internal/fsys/fsys.go b/src/cmd/go/internal/fsys/fsys.go
index e3a0e44f82d..0264786e5b2 100644
--- a/src/cmd/go/internal/fsys/fsys.go
+++ b/src/cmd/go/internal/fsys/fsys.go
@@ -327,12 +327,22 @@ func OverlayPath(path string) (string, bool) {
 
 // Open opens the file at or overlaid on the given path.
 func Open(path string) (*os.File, error) {
+	return OpenFile(path, os.O_RDONLY, 0)
+}
+
+// OpenFile opens the file at or overlaid on the given path with the flag and perm.
+func OpenFile(path string, flag int, perm os.FileMode) (*os.File, error) {
 	cpath := canonicalize(path)
 	if node, ok := overlay[cpath]; ok {
+		// Opening a file in the overlay.
 		if node.isDir() {
-			return nil, &fs.PathError{Op: "Open", Path: path, Err: errors.New("fsys.Open doesn't support opening directories yet")}
+			return nil, &fs.PathError{Op: "OpenFile", Path: path, Err: errors.New("fsys.OpenFile doesn't support opening directories yet")}
 		}
-		return os.Open(node.actualFilePath)
+		// We can't open overlaid paths for write.
+		if perm != os.FileMode(os.O_RDONLY) {
+			return nil, &fs.PathError{Op: "OpenFile", Path: path, Err: errors.New("overlaid files can't be opened for write")}
+		}
+		return os.OpenFile(node.actualFilePath, flag, perm)
 	}
 	if parent, ok := parentIsOverlayFile(filepath.Dir(cpath)); ok {
 		// The file is deleted explicitly in the Replace map,
@@ -344,7 +354,7 @@ func Open(path string) (*os.File, error) {
 			Err:  fmt.Errorf("file %s does not exist: parent directory %s is replaced by a file in overlay", path, parent),
 		}
 	}
-	return os.Open(cpath)
+	return os.OpenFile(cpath, flag, perm)
 }
 
 // IsDirWithGoFiles reports whether dir is a directory containing Go files
diff --git a/src/cmd/go/internal/lockedfile/lockedfile_filelock.go b/src/cmd/go/internal/lockedfile/lockedfile_filelock.go
index 10e1240efdd..efc66461ed2 100644
--- a/src/cmd/go/internal/lockedfile/lockedfile_filelock.go
+++ b/src/cmd/go/internal/lockedfile/lockedfile_filelock.go
@@ -10,6 +10,7 @@ import (
 	"io/fs"
 	"os"
 
+	"cmd/go/internal/fsys"
 	"cmd/go/internal/lockedfile/internal/filelock"
 )
 
@@ -19,7 +20,7 @@ func openFile(name string, flag int, perm fs.FileMode) (*os.File, error) {
 	// calls for Linux and Windows anyway, so it's simpler to use that approach
 	// consistently.
 
-	f, err := os.OpenFile(name, flag&^os.O_TRUNC, perm)
+	f, err := fsys.OpenFile(name, flag&^os.O_TRUNC, perm)
 	if err != nil {
 		return nil, err
 	}
diff --git a/src/cmd/go/internal/lockedfile/lockedfile_plan9.go b/src/cmd/go/internal/lockedfile/lockedfile_plan9.go
index 51681381d76..70d6eddf2d2 100644
--- a/src/cmd/go/internal/lockedfile/lockedfile_plan9.go
+++ b/src/cmd/go/internal/lockedfile/lockedfile_plan9.go
@@ -12,6 +12,8 @@ import (
 	"os"
 	"strings"
 	"time"
+
+	"cmd/go/internal/fsys"
 )
 
 // Opening an exclusive-use file returns an error.
@@ -56,7 +58,7 @@ func openFile(name string, flag int, perm fs.FileMode) (*os.File, error) {
 	// If the file was unpacked or created by some other program, it might not
 	// have the ModeExclusive bit set. Set it before we call OpenFile, so that we
 	// can be confident that a successful OpenFile implies exclusive use.
-	if fi, err := os.Stat(name); err == nil {
+	if fi, err := fsys.Stat(name); err == nil {
 		if fi.Mode()&fs.ModeExclusive == 0 {
 			if err := os.Chmod(name, fi.Mode()|fs.ModeExclusive); err != nil {
 				return nil, err
@@ -69,7 +71,7 @@ func openFile(name string, flag int, perm fs.FileMode) (*os.File, error) {
 	nextSleep := 1 * time.Millisecond
 	const maxSleep = 500 * time.Millisecond
 	for {
-		f, err := os.OpenFile(name, flag, perm|fs.ModeExclusive)
+		f, err := fsys.OpenFile(name, flag, perm|fs.ModeExclusive)
 		if err == nil {
 			return f, nil
 		}
diff --git a/src/cmd/go/internal/modcmd/vendor.go b/src/cmd/go/internal/modcmd/vendor.go
index 4e73960e80d..38c473d36be 100644
--- a/src/cmd/go/internal/modcmd/vendor.go
+++ b/src/cmd/go/internal/modcmd/vendor.go
@@ -18,6 +18,7 @@ import (
 
 	"cmd/go/internal/base"
 	"cmd/go/internal/cfg"
+	"cmd/go/internal/fsys"
 	"cmd/go/internal/imports"
 	"cmd/go/internal/modload"
 
@@ -259,7 +260,7 @@ func matchPotentialSourceFile(dir string, info fs.FileInfo) bool {
 		return false
 	}
 	if strings.HasSuffix(info.Name(), ".go") {
-		f, err := os.Open(filepath.Join(dir, info.Name()))
+		f, err := fsys.Open(filepath.Join(dir, info.Name()))
 		if err != nil {
 			base.Fatalf("go mod vendor: %v", err)
 		}
diff --git a/src/cmd/go/internal/modload/import.go b/src/cmd/go/internal/modload/import.go
index eb0a366f924..ce5671728e0 100644
--- a/src/cmd/go/internal/modload/import.go
+++ b/src/cmd/go/internal/modload/import.go
@@ -477,7 +477,7 @@ func dirInModule(path, mpath, mdir string, isLocal bool) (dir string, haveGoFile
 	if isLocal {
 		for d := dir; d != mdir && len(d) > len(mdir); {
 			haveGoMod := haveGoModCache.Do(d, func() interface{} {
-				fi, err := os.Stat(filepath.Join(d, "go.mod"))
+				fi, err := fsys.Stat(filepath.Join(d, "go.mod"))
 				return err == nil && !fi.IsDir()
 			}).(bool)
 
@@ -531,7 +531,7 @@ func fetch(ctx context.Context, mod module.Version, needSum bool) (dir string, i
 			// dirInModule does not report errors for missing modules,
 			// so if we don't report the error now, later failures will be
 			// very mysterious.
-			if _, err := os.Stat(dir); err != nil {
+			if _, err := fsys.Stat(dir); err != nil {
 				if os.IsNotExist(err) {
 					// Semantically the module version itself “exists” — we just don't
 					// have its source code. Remove the equivalence to os.ErrNotExist,
diff --git a/src/cmd/go/internal/modload/init.go b/src/cmd/go/internal/modload/init.go
index 8fe71a24487..b9345acbce2 100644
--- a/src/cmd/go/internal/modload/init.go
+++ b/src/cmd/go/internal/modload/init.go
@@ -206,7 +206,7 @@ func Init() {
 		base.Fatalf("missing $GOPATH")
 	}
 	gopath = list[0]
-	if _, err := os.Stat(filepath.Join(gopath, "go.mod")); err == nil {
+	if _, err := fsys.Stat(filepath.Join(gopath, "go.mod")); err == nil {
 		base.Fatalf("$GOPATH/go.mod exists but should not")
 	}
 
@@ -407,7 +407,7 @@ func CreateModFile(ctx context.Context, modPath string) {
 	modRoot = base.Cwd
 	Init()
 	modFilePath := ModFilePath()
-	if _, err := os.Stat(modFilePath); err == nil {
+	if _, err := fsys.Stat(modFilePath); err == nil {
 		base.Fatalf("go: %s already exists", modFilePath)
 	}
 
@@ -605,7 +605,7 @@ func setDefaultBuildMod() {
 		return
 	}
 
-	if fi, err := os.Stat(filepath.Join(modRoot, "vendor")); err == nil && fi.IsDir() {
+	if fi, err := fsys.Stat(filepath.Join(modRoot, "vendor")); err == nil && fi.IsDir() {
 		modGo := "unspecified"
 		if index.goVersionV != "" {
 			if semver.Compare(index.goVersionV, "v1.14") >= 0 {
@@ -685,7 +685,7 @@ func findModuleRoot(dir string) (root string) {
 
 	// Look for enclosing go.mod.
 	for {
-		if fi, err := os.Stat(filepath.Join(dir, "go.mod")); err == nil && !fi.IsDir() {
+		if fi, err := fsys.Stat(filepath.Join(dir, "go.mod")); err == nil && !fi.IsDir() {
 			return dir
 		}
 		d := filepath.Dir(dir)
@@ -709,7 +709,7 @@ func findAltConfig(dir string) (root, name string) {
 	}
 	for {
 		for _, name := range altConfigs {
-			if fi, err := os.Stat(filepath.Join(dir, name)); err == nil && !fi.IsDir() {
+			if fi, err := fsys.Stat(filepath.Join(dir, name)); err == nil && !fi.IsDir() {
 				return dir, name
 			}
 		}
diff --git a/src/cmd/go/internal/search/search.go b/src/cmd/go/internal/search/search.go
index 57cbb282a8b..18738cf59ec 100644
--- a/src/cmd/go/internal/search/search.go
+++ b/src/cmd/go/internal/search/search.go
@@ -295,7 +295,7 @@ func (m *Match) MatchDirs() {
 
 		if !top && cfg.ModulesEnabled {
 			// Ignore other modules found in subdirectories.
-			if fi, err := os.Stat(filepath.Join(path, "go.mod")); err == nil && !fi.IsDir() {
+			if fi, err := fsys.Stat(filepath.Join(path, "go.mod")); err == nil && !fi.IsDir() {
 				return filepath.SkipDir
 			}
 		}
diff --git a/src/cmd/go/testdata/script/mod_overlay.txt b/src/cmd/go/testdata/script/mod_overlay.txt
new file mode 100644
index 00000000000..35bb30248b0
--- /dev/null
+++ b/src/cmd/go/testdata/script/mod_overlay.txt
@@ -0,0 +1,248 @@
+# Test overlays that affect go.mod files
+
+# The go.mod file can exist only in the overlay.
+cd $WORK/gopath/src/no-go-mod
+go list -overlay overlay.json .
+stdout example.com/simple
+
+# Check content of overlaid go.mod is used.
+cd $WORK/gopath/src/overlay-go-mod
+go list -overlay overlay.json .
+stdout use.this/module/name
+
+# Check content of overlaid go.mod in a replacement module is used.
+# The go.mod in the replacement module is missing a requirement
+# that the overlay has, so it will fail to list without the overlay.
+cd $WORK/gopath/src/overlay-replaced-go-mod
+! go list -deps .
+go list -deps -overlay overlay.json .
+
+# Overlaid go.mod is not rewritten by 'go get'.
+cd $WORK/gopath/src/get-doesnt-add-dep
+cp $WORK/overlay/get_doesnt_add_dep_go_mod $WORK/want_go_mod
+! go get -d -overlay overlay.json .
+stderr 'overlaid files can''t be opened for write'
+cmp $WORK/overlay/get_doesnt_add_dep_go_mod $WORK/want_go_mod
+
+# Content of overlaid go.sum is used.
+# The go.sum in the module directory has garbage values for its
+# hashes, but the overlaid file has the correct values. If
+# the correct go.sum is used with the overlay, 'go get .' should
+# not report a security error.
+cd $WORK/gopath/src/overlay-sum-used
+! go get -d .
+stderr 'SECURITY ERROR'
+go get -d -overlay overlay.json .
+# Overlaid go.sum is not rewritten.
+# Copy an incomplete file to the overlay file, and expect an error
+# attempting to update the file
+cp incomplete-sum-file $WORK/overlay/overlay-sum-used-correct-sums
+! go get -d -overlay overlay.json .
+stderr 'overlaid files can''t be opened for write'
+cmp incomplete-sum-file $WORK/overlay/overlay-sum-used-correct-sums
+
+# -overlay works with -modfile.
+# There's an empty go.mod file in the directory, and the file alternate.mod is
+# overlaid to the true go.mod file, so the -modfile flag and the overlay
+# mechanism need to work together to determine the name of the module.
+cd $WORK/gopath/src/overlay-and-dash-modfile
+go list -modfile=alternate.mod -overlay overlay.json .
+stdout 'found.the/module'
+# Even with -modfile, overlaid files can't be opened for write.
+! go get -modfile=alternate.mod -overlay overlay.json -d rsc.io/quote
+stderr 'overlaid files can''t be opened for write'
+
+# Carving out a module by adding an overlaid go.mod file
+cd $WORK/gopath/src/carve
+go list ./... # without an overlay, hasmod is carved out and nomod isn't
+stdout carve/nomod
+! stdout carve/hasmod
+go list -overlay overlay_carve_module.json ./... # The overlay carves out nomod, leaving nothing
+! stdout .
+stderr 'matched no packages'
+go list -overlay overlay_uncarve_module.json ./... # The overlay uncarves out hasmod
+stdout carve/nomod
+stdout carve/hasmod
+
+# Carving out a module by adding an overlaid go.mod file and using
+# -modfile to write to that file.
+cd $WORK/gopath/src/carve2/nomod
+go list -overlay overlay.json all
+! stdout ^carve2$
+stdout ^carve2/nomod$
+# Editing go.mod file fails because overlay is read only
+! go get -overlay overlay.json -d rsc.io/quote
+stderr 'overlaid files can''t be opened for write'
+! grep rsc.io/quote $WORK/overlay/carve2-nomod-go.mod
+# Editing go.mod file succeeds because we use -modfile to redirect to same file
+go get -overlay overlay.json -modfile $WORK/overlay/carve2-nomod-go.mod -d rsc.io/quote
+grep rsc.io/quote $WORK/overlay/carve2-nomod-go.mod
+
+-- no-go-mod/file.go --
+package simple
+-- no-go-mod/overlay.json --
+{
+	"Replace": {
+		"go.mod": "../../../overlay/simple_go_mod"
+	}
+}
+-- $WORK/overlay/simple_go_mod --
+module example.com/simple
+-- overlay-go-mod/file.go --
+package name
+-- overlay-go-mod/go.mod --
+module dont.use/this/module/name
+-- overlay-go-mod/overlay.json --
+{
+	"Replace": {
+		"go.mod": "../../../overlay/use_this_go_mod"
+	}
+}
+-- $WORK/overlay/use_this_go_mod --
+module use.this/module/name
+-- overlay-replaced-go-mod/go.mod --
+module m
+
+go 1.15
+
+require replaced/mod v1.0.0
+replace replaced/mod v1.0.0 => ../replaced-mod
+replace dep/mod v1.0.0 => ../dep-mod
+-- overlay-replaced-go-mod/source.go --
+package m
+
+import "replaced/mod/foo"
+
+func main() {
+	foo.f()
+}
+-- overlay-replaced-go-mod/overlay.json --
+{
+	"Replace": {
+		"../replaced-mod/go.mod": "../../../overlay/replacement_module_go_mod"
+	}
+}
+-- replaced-mod/go.mod --
+module replaced/mod
+-- replaced-mod/foo/foo.go --
+package foo
+
+import "dep/mod/foo"
+
+func f() { foo.g() }
+-- dep-mod/go.mod --
+invalid
+-- dep-mod/foo/foo.go --
+package foo
+
+func g() { fmt.Println("hello") }
+-- $WORK/overlay/replacement_module_go_mod --
+module replaced/mod
+
+require dep/mod v1.0.0
+
+-- get-doesnt-add-dep/overlay.json --
+{
+	"Replace": {
+		"go.mod": "../../../overlay/get_doesnt_add_dep_go_mod"
+	}
+}
+-- get-doesnt-add-dep/p.go --
+package p
+
+import "dependency/mod"
+
+func f() { mod.G() }
+-- get-doesnt-add-dep-dependency/go.mod --
+module dependency/mod
+-- get-doesnt-add-dep-dependency/mod.go --
+package mod
+
+func G() {}
+-- $WORK/overlay/get_doesnt_add_dep_go_mod --
+module get.doesnt/add/dep
+
+replace dependency/mod v1.0.0 => ../get-doesnt-add-dep-dependency
+-- overlay-sum-used/go.mod --
+module overlay.sum/used
+
+require rsc.io/quote v1.5.0
+-- overlay-sum-used/p.go --
+package p
+
+import "rsc.io/quote"
+
+func f() string {
+	return quote.Hello()
+}
+-- overlay-sum-used/incomplete-sum-file --
+golang.org/x/text v0.0.0-20170915032832-14c0d48ead0c h1:pvCbr/wm8HzDD3fVywevekufpn6tCGPY3spdHeZJEsw=
+rsc.io/quote v1.5.0 h1:6fJa6E+wGadANKkUMlZ0DhXFpoKlslOQDCo259XtdIE=
+rsc.io/sampler v1.3.0 h1:HLGR/BgEtI3r0uymSP/nl2uPLsUnNJX8toRyhfpBTII=
+-- overlay-sum-used/overlay.json --
+{
+	"Replace": {
+		"go.sum": "../../../overlay/overlay-sum-used-correct-sums"
+	}
+}
+-- overlay-sum-used/go.sum --
+golang.org/x/text v0.0.0-20170915032832-14c0d48ead0c h1:garbage+hash
+golang.org/x/text v0.0.0-20170915032832-14c0d48ead0c/go.mod h1:garbage+hash
+rsc.io/quote v1.5.0 h1:garbage+hash
+rsc.io/quote v1.5.0/go.mod h1:garbage+hash
+rsc.io/sampler v1.3.0 h1:garbage+hash
+rsc.io/sampler v1.3.0/go.mod h1:garbage+hash
+-- $WORK/overlay/overlay-sum-used-correct-sums --
+golang.org/x/text v0.0.0-20170915032832-14c0d48ead0c h1:pvCbr/wm8HzDD3fVywevekufpn6tCGPY3spdHeZJEsw=
+golang.org/x/text v0.0.0-20170915032832-14c0d48ead0c/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
+rsc.io/quote v1.5.0 h1:6fJa6E+wGadANKkUMlZ0DhXFpoKlslOQDCo259XtdIE=
+rsc.io/quote v1.5.0/go.mod h1:LzX7hefJvL54yjefDEDHNONDjII0t9xZLPXsUe+TKr0=
+rsc.io/sampler v1.3.0 h1:HLGR/BgEtI3r0uymSP/nl2uPLsUnNJX8toRyhfpBTII=
+rsc.io/sampler v1.3.0/go.mod h1:T1hPZKmBbMNahiBKFy5HrXp6adAjACjK9JXDnKaTXpA=
+-- overlay-and-dash-modfile/p.go --
+package module
+-- overlay-and-dash-modfile/go.mod --
+-- overlay-and-dash-modfile/overlay.json --
+{
+	"Replace": {
+		"alternate.mod": "../../../overlay/overlay-and-dash-modfile-alternate-mod"
+	}
+}
+-- $WORK/overlay/overlay-and-dash-modfile-alternate-mod --
+module found.the/module
+-- carve/go.mod --
+module carve
+-- carve/overlay_carve_module.json --
+{
+	"Replace": {
+		"nomod/go.mod": "../../../overlay/carve-nomod-go-mod"
+	}
+}
+-- carve/overlay_uncarve_module.json --
+{
+	"Replace": {
+		"hasmod/go.mod": ""
+	}
+}
+-- carve/hasmod/a.go --
+package hasmod
+-- carve/hasmod/go.mod --
+module carve/hasmod
+-- carve/nomod/b.go --
+package nomod
+-- $WORK/overlay/carve-nomod-go-mod --
+module carve/nomod
+-- carve2/go.mod --
+module carve2
+-- carve2/p.go --
+package p
+-- carve2/nomod/overlay.json --
+{
+	"Replace": {
+		"go.mod": "../../../../overlay/carve2-nomod-go.mod"
+	}
+}
+-- carve2/nomod/b.go --
+package nomod
+-- $WORK/overlay/carve2-nomod-go.mod --
+module carve2/nomod