diff --git a/enterprise/causal-clustering/src/main/java/org/neo4j/causalclustering/catchup/storecopy/StoreCopyClient.java b/enterprise/causal-clustering/src/main/java/org/neo4j/causalclustering/catchup/storecopy/StoreCopyClient.java
index 72d883d3f0de6..e83cf93bcb9ec 100644
--- a/enterprise/causal-clustering/src/main/java/org/neo4j/causalclustering/catchup/storecopy/StoreCopyClient.java
+++ b/enterprise/causal-clustering/src/main/java/org/neo4j/causalclustering/catchup/storecopy/StoreCopyClient.java
@@ -69,7 +69,6 @@ long copyStoreFiles( CatchupAddressProvider catchupAddressProvider, StoreId expe
     private void copyFilesIndividually( PrepareStoreCopyResponse prepareStoreCopyResponse, StoreId expectedStoreId, CatchupAddressProvider addressProvider,
             StoreFileStreamProvider storeFileStream, Supplier<TerminationCondition> terminationConditions ) throws StoreCopyFailedException
     {
-        CatchUpResponseAdaptor<StoreCopyFinishedResponse> copyHandler = StoreCopyResponseAdaptors.filesCopyAdaptor( storeFileStream, log );
         long lastTransactionId = prepareStoreCopyResponse.lastTransactionId();
         for ( File file : prepareStoreCopyResponse.getFiles() )
         {
@@ -82,7 +81,8 @@ private void copyFilesIndividually( PrepareStoreCopyResponse prepareStoreCopyRes
                     AdvertisedSocketAddress from = addressProvider.primary();
                     log.info( format( "Downloading file '%s' from '%s'", file, from ) );
                     StoreCopyFinishedResponse response =
-                            catchUpClient.makeBlockingRequest( from, new GetStoreFileRequest( expectedStoreId, file, lastTransactionId ), copyHandler );
+                            catchUpClient.makeBlockingRequest( from, new GetStoreFileRequest( expectedStoreId, file, lastTransactionId ),
+                                    StoreCopyResponseAdaptors.filesCopyAdaptor( storeFileStream, log ) );
                     successful = successfulFileDownload( response );
                 }
                 catch ( CatchUpClientException | CatchupAddressResolutionException e )
@@ -103,7 +103,6 @@ private void copyIndexSnapshotIndividually( PrepareStoreCopyResponse prepareStor
             CatchupAddressProvider addressProvider, StoreFileStreamProvider storeFileStream, Supplier<TerminationCondition> terminationConditions )
             throws StoreCopyFailedException
     {
-        CatchUpResponseAdaptor<StoreCopyFinishedResponse> copyHandler = StoreCopyResponseAdaptors.filesCopyAdaptor( storeFileStream, log );
         long lastTransactionId = prepareStoreCopyResponse.lastTransactionId();
         PrimitiveLongIterator indexIds = prepareStoreCopyResponse.getIndexIds().iterator();
         while ( indexIds.hasNext() )
@@ -119,7 +118,7 @@ private void copyIndexSnapshotIndividually( PrepareStoreCopyResponse prepareStor
                     log.info( format( "Downloading snapshot of index '%s' from '%s'", indexId, from ) );
                     StoreCopyFinishedResponse response =
                             catchUpClient.makeBlockingRequest( from, new GetIndexFilesRequest( expectedStoreId, indexId, lastTransactionId ),
-                                    copyHandler );
+                                    StoreCopyResponseAdaptors.filesCopyAdaptor( storeFileStream, log ) );
                     successful = successfulFileDownload( response );
                 }
                 catch ( CatchUpClientException | CatchupAddressResolutionException e )
diff --git a/enterprise/causal-clustering/src/main/java/org/neo4j/causalclustering/catchup/storecopy/StoreCopyResponseAdaptors.java b/enterprise/causal-clustering/src/main/java/org/neo4j/causalclustering/catchup/storecopy/StoreCopyResponseAdaptors.java
index 1da1aac517f48..f3037d8f77e0f 100644
--- a/enterprise/causal-clustering/src/main/java/org/neo4j/causalclustering/catchup/storecopy/StoreCopyResponseAdaptors.java
+++ b/enterprise/causal-clustering/src/main/java/org/neo4j/causalclustering/catchup/storecopy/StoreCopyResponseAdaptors.java
@@ -20,10 +20,13 @@
 package org.neo4j.causalclustering.catchup.storecopy;
 
 import java.util.concurrent.CompletableFuture;
+import java.util.function.BiConsumer;
 
 import org.neo4j.causalclustering.catchup.CatchUpResponseAdaptor;
 import org.neo4j.logging.Log;
 
+import static java.lang.String.format;
+
 public abstract class StoreCopyResponseAdaptors<T> extends CatchUpResponseAdaptor<T>
 {
     static StoreCopyResponseAdaptors<StoreCopyFinishedResponse> filesCopyAdaptor( StoreFileStreamProvider storeFileStreamProvider, Log log )
@@ -46,23 +49,21 @@ private StoreCopyResponseAdaptors( StoreFileStreamProvider storeFileStreamProvid
         this.log = log;
     }
 
+    /**
+     * Files will be sent in order but multiple files may be sent during one response.
+     *
+     * @param requestOutcomeSignal signal
+     * @param fileHeader header for most resent file being sent
+     */
     @Override
     public void onFileHeader( CompletableFuture<T> requestOutcomeSignal, FileHeader fileHeader )
     {
         try
         {
-            storeFileStream = storeFileStreamProvider.acquire( fileHeader.fileName(), fileHeader.requiredAlignment() );
-            requestOutcomeSignal.whenComplete( ( storeCopyFinishedResponse, throwable ) ->
-            {
-                try
-                {
-                    storeFileStream.close();
-                }
-                catch ( Exception e )
-                {
-                    log.error( "Unable to close store file stream", e );
-                }
-            } );
+            final StoreFileStream fileStream = storeFileStreamProvider.acquire( fileHeader.fileName(), fileHeader.requiredAlignment() );
+            // Make sure that each stream closes on complete but only the latest is written to
+            requestOutcomeSignal.whenComplete( new CloseFileStreamOnComplete<>( fileStream, fileHeader.fileName() ) );
+            this.storeFileStream = fileStream;
         }
         catch ( Exception e )
         {
@@ -111,4 +112,29 @@ public void onFileStreamingComplete( CompletableFuture<StoreCopyFinishedResponse
             signal.complete( response );
         }
     }
+
+    private class CloseFileStreamOnComplete<RESPONSE> implements BiConsumer<RESPONSE,Throwable>
+    {
+        private final StoreFileStream fileStream;
+        private String fileName;
+
+        private CloseFileStreamOnComplete( StoreFileStream fileStream, String fileName )
+        {
+            this.fileStream = fileStream;
+            this.fileName = fileName;
+        }
+
+        @Override
+        public void accept( RESPONSE response, Throwable throwable )
+        {
+            try
+            {
+                fileStream.close();
+            }
+            catch ( Exception e )
+            {
+                log.error( format( "Unable to close store file stream for file '%s'", fileName ), e );
+            }
+        }
+    }
 }