diff --git a/src/libstore-c/nix_api_store.cc b/src/libstore-c/nix_api_store.cc
index 024ed97858a..6fd3bb6f588 100644
--- a/src/libstore-c/nix_api_store.cc
+++ b/src/libstore-c/nix_api_store.cc
@@ -251,7 +251,7 @@ nix_err nix_store_copy_closure(nix_c_context * context, Store * srcStore, Store
     if (context)
         context->last_err_code = NIX_OK;
     try {
-        nix::RealisedPath::Set paths;
+        nix::StorePathSet paths;
         paths.insert(path->path);
         nix::copyClosure(*srcStore->ptr, *dstStore->ptr, paths);
     }
diff --git a/src/libstore/include/nix/store/legacy-ssh-store.hh b/src/libstore/include/nix/store/legacy-ssh-store.hh
index 994918f90f0..47e505ba1d6 100644
--- a/src/libstore/include/nix/store/legacy-ssh-store.hh
+++ b/src/libstore/include/nix/store/legacy-ssh-store.hh
@@ -175,7 +175,8 @@ public:
         StorePathSet & out,
         bool flipDirection = false,
         bool includeOutputs = false,
-        bool includeDerivers = false) override;
+        bool includeDerivers = false,
+        std::function<bool(const StorePath & path)> pathCallback = nullptr) override;
 
     StorePathSet queryValidPaths(const StorePathSet & paths, SubstituteFlag maybeSubstitute = NoSubstitute) override;
 
diff --git a/src/libstore/include/nix/store/store-api.hh b/src/libstore/include/nix/store/store-api.hh
index 4c0b156faaa..80c03f170d6 100644
--- a/src/libstore/include/nix/store/store-api.hh
+++ b/src/libstore/include/nix/store/store-api.hh
@@ -802,13 +802,19 @@ public:
      * `storePath` is returned; that is, the closures under the
      * `referrers` relation instead of the `references` relation is
      * returned.
+     *
+     * @param onPathDiscovered A callback invoked on each discovered store
+     * path. Returning `false` from the callback will stop recursion on
+     * that path. Returning `true` will continue recursion. A `nullptr` is
+     * equivalent to a callback which always returns  `true`.
      */
     virtual void computeFSClosure(
         const StorePathSet & paths,
         StorePathSet & out,
         bool flipDirection = false,
         bool includeOutputs = false,
-        bool includeDerivers = false);
+        bool includeDerivers = false,
+        std::function<bool(const StorePath & path)> onPathDiscovered = nullptr);
 
     void computeFSClosure(
         const StorePath & path,
diff --git a/src/libstore/legacy-ssh-store.cc b/src/libstore/legacy-ssh-store.cc
index 3b466c9bb8b..cbf5955b4a0 100644
--- a/src/libstore/legacy-ssh-store.cc
+++ b/src/libstore/legacy-ssh-store.cc
@@ -252,10 +252,15 @@ void LegacySSHStore::buildPaths(
 }
 
 void LegacySSHStore::computeFSClosure(
-    const StorePathSet & paths, StorePathSet & out, bool flipDirection, bool includeOutputs, bool includeDerivers)
+    const StorePathSet & paths,
+    StorePathSet & out,
+    bool flipDirection,
+    bool includeOutputs,
+    bool includeDerivers,
+    std::function<bool(const StorePath & path)> onPathDiscovered)
 {
-    if (flipDirection || includeDerivers) {
-        Store::computeFSClosure(paths, out, flipDirection, includeOutputs, includeDerivers);
+    if (flipDirection || includeDerivers || onPathDiscovered) {
+        Store::computeFSClosure(paths, out, flipDirection, includeOutputs, includeDerivers, onPathDiscovered);
         return;
     }
 
diff --git a/src/libstore/misc.cc b/src/libstore/misc.cc
index ca2458302d6..8ff4a2bf5f4 100644
--- a/src/libstore/misc.cc
+++ b/src/libstore/misc.cc
@@ -21,7 +21,8 @@ void Store::computeFSClosure(
     StorePathSet & paths_,
     bool flipDirection,
     bool includeOutputs,
-    bool includeDerivers)
+    bool includeDerivers,
+    std::function<bool(const StorePath & path)> onPathDiscovered)
 {
     std::function<std::set<StorePath>(const StorePath & path, std::future<ref<const ValidPathInfo>> &)> queryDeps;
     if (flipDirection)
@@ -65,6 +66,12 @@ void Store::computeFSClosure(
         startPaths,
         paths_,
         [&](const StorePath & path, std::function<void(std::promise<std::set<StorePath>> &)> processEdges) {
+            if (onPathDiscovered && !onPathDiscovered(path)) {
+                std::promise<std::set<StorePath>> promise;
+                promise.set_value({});
+                processEdges(promise);
+                return;
+            }
             std::promise<std::set<StorePath>> promise;
             std::function<void(std::future<ref<const ValidPathInfo>>)> getDependencies =
                 [&](std::future<ref<const ValidPathInfo>> fut) {
diff --git a/src/libstore/store-api.cc b/src/libstore/store-api.cc
index c292e2e431d..ef1ecf970ea 100644
--- a/src/libstore/store-api.cc
+++ b/src/libstore/store-api.cc
@@ -1072,9 +1072,16 @@ void copyClosure(
     if (&srcStore == &dstStore)
         return;
 
-    StorePathSet closure;
-    srcStore.computeFSClosure(storePaths, closure);
-    copyPaths(srcStore, dstStore, closure, repair, checkSigs, substitute);
+    StorePathSet pathsToCopy;
+
+    auto onPathDiscovered = [&](const StorePath & path) -> bool {
+        // Only recurse if the path does not already exist in `dstStore`
+        return repair || !dstStore.isValidPath(path);
+    };
+    srcStore.computeFSClosure(storePaths, pathsToCopy, false, false, false, onPathDiscovered);
+    pathsToCopy.insert(storePaths.begin(), storePaths.end());
+
+    copyPaths(srcStore, dstStore, pathsToCopy, repair, checkSigs, substitute);
 }
 
 std::optional<ValidPathInfo>