diff --git a/Ghidra/Features/Base/src/main/java/ghidra/app/plugin/core/graph/GraphDisplayBrokerPlugin.java b/Ghidra/Features/Base/src/main/java/ghidra/app/plugin/core/graph/GraphDisplayBrokerPlugin.java
index d7922ee835..a9cc27d188 100644
--- a/Ghidra/Features/Base/src/main/java/ghidra/app/plugin/core/graph/GraphDisplayBrokerPlugin.java
+++ b/Ghidra/Features/Base/src/main/java/ghidra/app/plugin/core/graph/GraphDisplayBrokerPlugin.java
@@ -4,9 +4,9 @@
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
- * 
+ *
  *      http://www.apache.org/licenses/LICENSE-2.0
- * 
+ *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
@@ -151,7 +151,7 @@ public class GraphDisplayBrokerPlugin extends Plugin
 	public GraphDisplay getDefaultGraphDisplay(boolean reuseGraph, TaskMonitor monitor)
 			throws GraphException {
 		if (defaultGraphDisplayProvider != null) {
-			return defaultGraphDisplayProvider.getGraphDisplay(reuseGraph, monitor);
+			return defaultGraphDisplayProvider.getGraphDisplay(reuseGraph, false, monitor);
 		}
 		return null;
 	}
diff --git a/Ghidra/Features/GraphServices/src/main/java/ghidra/graph/export/ExportAttributedGraphDisplayProvider.java b/Ghidra/Features/GraphServices/src/main/java/ghidra/graph/export/ExportAttributedGraphDisplayProvider.java
index 8dc952b1f3..24de24efeb 100644
--- a/Ghidra/Features/GraphServices/src/main/java/ghidra/graph/export/ExportAttributedGraphDisplayProvider.java
+++ b/Ghidra/Features/GraphServices/src/main/java/ghidra/graph/export/ExportAttributedGraphDisplayProvider.java
@@ -4,9 +4,9 @@
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
- * 
+ *
  *      http://www.apache.org/licenses/LICENSE-2.0
- * 
+ *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
@@ -52,8 +52,7 @@ public class ExportAttributedGraphDisplayProvider implements GraphDisplayProvide
 	}
 
 	@Override
-	public GraphDisplay getGraphDisplay(boolean reuseGraph,
-			TaskMonitor monitor) {
+	public GraphDisplay getGraphDisplay(boolean reuseGraph, boolean append, TaskMonitor monitor) {
 		return new ExportAttributedGraphDisplay(this);
 	}
 
diff --git a/Ghidra/Features/GraphServices/src/main/java/ghidra/graph/visualization/DefaultGraphDisplay.java b/Ghidra/Features/GraphServices/src/main/java/ghidra/graph/visualization/DefaultGraphDisplay.java
index 59954c39e0..f736a01fb4 100644
--- a/Ghidra/Features/GraphServices/src/main/java/ghidra/graph/visualization/DefaultGraphDisplay.java
+++ b/Ghidra/Features/GraphServices/src/main/java/ghidra/graph/visualization/DefaultGraphDisplay.java
@@ -568,7 +568,8 @@ public class DefaultGraphDisplay implements GraphDisplay {
 	}
 
 	private void createAndDisplaySubGraph() {
-		GraphDisplay display = graphDisplayProvider.getGraphDisplay(false, TaskMonitor.DUMMY);
+		GraphDisplay display =
+			graphDisplayProvider.getGraphDisplay(false, false, TaskMonitor.DUMMY);
 		try {
 			display.setGraph(createSubGraph(), graphRenderer.getGraphDisplayOptions(),
 				title + " - Sub-graph", false, TaskMonitor.DUMMY);
@@ -1065,7 +1066,8 @@ public class DefaultGraphDisplay implements GraphDisplay {
 	public void setGraph(AttributedGraph graph, GraphDisplayOptions options, String title,
 			boolean append, TaskMonitor monitor) {
 		setGraphDisplayOptions(options);
-		if (append && Objects.equals(title, this.title) && this.graph != null) {
+		if (append && this.graph != null &&
+			graph.getGraphType().equals(this.graph.getGraphType())) {
 			graph = mergeGraphs(graph, this.graph);
 		}
 
diff --git a/Ghidra/Features/GraphServices/src/main/java/ghidra/graph/visualization/DefaultGraphDisplayProvider.java b/Ghidra/Features/GraphServices/src/main/java/ghidra/graph/visualization/DefaultGraphDisplayProvider.java
index 91e127ab69..e790516dc5 100644
--- a/Ghidra/Features/GraphServices/src/main/java/ghidra/graph/visualization/DefaultGraphDisplayProvider.java
+++ b/Ghidra/Features/GraphServices/src/main/java/ghidra/graph/visualization/DefaultGraphDisplayProvider.java
@@ -4,9 +4,9 @@
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
- * 
+ *
  *      http://www.apache.org/licenses/LICENSE-2.0
- * 
+ *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
@@ -52,7 +52,7 @@ public class DefaultGraphDisplayProvider implements GraphDisplayProvider {
 	}
 
 	@Override
-	public GraphDisplay getGraphDisplay(boolean reuseGraph, TaskMonitor monitor) {
+	public GraphDisplay getGraphDisplay(boolean reuseGraph, boolean append, TaskMonitor monitor) {
 
 		return Swing.runNow(() -> {
 
@@ -61,9 +61,15 @@ public class DefaultGraphDisplayProvider implements GraphDisplayProvider {
 					(DefaultGraphDisplayWrapper) getActiveGraphDisplay();
 
 				// set a temporary dummy graph; clients will set a real graph
-				visibleGraph.setGraph(new AttributedGraph("Empty", null),
-					new DefaultGraphDisplayOptions(), "", false, monitor);
-				visibleGraph.restoreDefaultState();
+				if (!append) {
+					// only clear the graph if we aren't appending. We did the clear in case
+					// it was laying out the graph and nodes got yanked out from under it, but
+					// if the intention is to append to the graph, all existing nodes will still
+					// be there, so no stack trace attempting to access a missing vertex.
+					visibleGraph.setGraph(new AttributedGraph("Empty", null),
+						new DefaultGraphDisplayOptions(), "", false, monitor);
+					visibleGraph.restoreDefaultState();
+				}
 				return visibleGraph;
 			}
 
diff --git a/Ghidra/Features/ProgramGraph/src/main/java/ghidra/graph/program/BlockGraphTask.java b/Ghidra/Features/ProgramGraph/src/main/java/ghidra/graph/program/BlockGraphTask.java
index d3feafef3b..446b9ab79c 100644
--- a/Ghidra/Features/ProgramGraph/src/main/java/ghidra/graph/program/BlockGraphTask.java
+++ b/Ghidra/Features/ProgramGraph/src/main/java/ghidra/graph/program/BlockGraphTask.java
@@ -4,9 +4,9 @@
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
- * 
+ *
  *      http://www.apache.org/licenses/LICENSE-2.0
- * 
+ *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
@@ -93,7 +93,7 @@ public class BlockGraphTask extends Task {
 		AttributedGraph graph = createGraph(graphTitle);
 		monitor.setMessage("Generating Graph...");
 		try {
-			GraphDisplay display = graphProvider.getGraphDisplay(reuseGraph, monitor);
+			GraphDisplay display = graphProvider.getGraphDisplay(reuseGraph, appendGraph, monitor);
 			GraphDisplayOptions graphOptions = new ProgramGraphDisplayOptions(graphType, tool);
 			if (showCode) { // arrows need to be bigger as this generates larger vertices
 				graphOptions.setArrowLength(30);
diff --git a/Ghidra/Features/ProgramGraph/src/main/java/ghidra/graph/program/DataReferenceGraphTask.java b/Ghidra/Features/ProgramGraph/src/main/java/ghidra/graph/program/DataReferenceGraphTask.java
index c616130436..6d29dbf3d4 100644
--- a/Ghidra/Features/ProgramGraph/src/main/java/ghidra/graph/program/DataReferenceGraphTask.java
+++ b/Ghidra/Features/ProgramGraph/src/main/java/ghidra/graph/program/DataReferenceGraphTask.java
@@ -4,9 +4,9 @@
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
- * 
+ *
  *      http://www.apache.org/licenses/LICENSE-2.0
- * 
+ *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
@@ -130,7 +130,7 @@ public class DataReferenceGraphTask extends Task {
 
 		try {
 			if (display == null) {
-				display = graphProvider.getGraphDisplay(reuseGraph, monitor);
+				display = graphProvider.getGraphDisplay(reuseGraph, appendGraph, monitor);
 
 				DataReferenceGraphDisplayListener listener =
 					new DataReferenceGraphDisplayListener(tool, display, program, totalMaxDepth);
diff --git a/Ghidra/Framework/SoftwareModeling/src/main/java/ghidra/service/graph/GraphDisplayProvider.java b/Ghidra/Framework/SoftwareModeling/src/main/java/ghidra/service/graph/GraphDisplayProvider.java
index b460ab7f70..33d7edbc4e 100644
--- a/Ghidra/Framework/SoftwareModeling/src/main/java/ghidra/service/graph/GraphDisplayProvider.java
+++ b/Ghidra/Framework/SoftwareModeling/src/main/java/ghidra/service/graph/GraphDisplayProvider.java
@@ -4,9 +4,9 @@
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
- * 
+ *
  *      http://www.apache.org/licenses/LICENSE-2.0
- * 
+ *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
@@ -38,12 +38,34 @@ public interface GraphDisplayProvider extends ExtensionPoint {
 	/**
 	 * Returns a GraphDisplay that can be used to "display" a graph
 	 * 
-	 * @param reuseGraph if true, this provider will attempt to re-use an existing GraphDisplay
+	 * @param reuseGraph if true, this provider will attempt to re-use an existing GraphDisplay.
+	 * Note: this form will always clear the graph. If the intention is to append to the graph,
+	 * use the {@link #getGraphDisplay(boolean, boolean, TaskMonitor)} method instead.
+	 * so that it can be appended to. Otherwise, any reused graph display will be have its 
+	 * existing graph cleared.
+	 * 
 	 * @param monitor the {@link TaskMonitor} that can be used to monitor and cancel the operation
 	 * @return an object that can be used to display or otherwise consume (e.g., export) the graph
 	 * @throws GraphException thrown if there is a problem creating a GraphDisplay
 	 */
-	public GraphDisplay getGraphDisplay(boolean reuseGraph, TaskMonitor monitor)
+	public default GraphDisplay getGraphDisplay(boolean reuseGraph, TaskMonitor monitor)
+			throws GraphException {
+		return getGraphDisplay(reuseGraph, false, monitor);
+	}
+
+	/**
+	 * Returns a GraphDisplay that can be used to "display" a graph
+	 * 
+	 * @param reuseGraph if true, this provider will attempt to re-use an existing GraphDisplay
+	 * @param append if true and there is a graph display to reuse, don't clear the existing graph
+	 * so that it can be appended to. Otherwise, any reused graph display will be have its 
+	 * existing graph cleared.
+	 * 
+	 * @param monitor the {@link TaskMonitor} that can be used to monitor and cancel the operation
+	 * @return an object that can be used to display or otherwise consume (e.g., export) the graph
+	 * @throws GraphException thrown if there is a problem creating a GraphDisplay
+	 */
+	public GraphDisplay getGraphDisplay(boolean reuseGraph, boolean append, TaskMonitor monitor)
 			throws GraphException;
 
 	/**
diff --git a/Ghidra/Test/IntegrationTest/src/test/java/ghidra/graph/TestGraphService.java b/Ghidra/Test/IntegrationTest/src/test/java/ghidra/graph/TestGraphService.java
index 41732e64b5..d9c7d1fe78 100644
--- a/Ghidra/Test/IntegrationTest/src/test/java/ghidra/graph/TestGraphService.java
+++ b/Ghidra/Test/IntegrationTest/src/test/java/ghidra/graph/TestGraphService.java
@@ -4,9 +4,9 @@
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
- * 
+ *
  *      http://www.apache.org/licenses/LICENSE-2.0
- * 
+ *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
@@ -35,7 +35,7 @@ public class TestGraphService implements GraphDisplayProvider {
 	}
 
 	@Override
-	public GraphDisplay getGraphDisplay(boolean reuseGraph,
+	public GraphDisplay getGraphDisplay(boolean reuseGraph, boolean append,
 			TaskMonitor monitor) throws GraphException {
 		return testDisplay;
 	}
diff --git a/Ghidra/Test/IntegrationTest/src/test/java/ghidra/graph/program/BlockGraphTaskTest.java b/Ghidra/Test/IntegrationTest/src/test/java/ghidra/graph/program/BlockGraphTaskTest.java
index 14d4f9ca51..01f4dee773 100644
--- a/Ghidra/Test/IntegrationTest/src/test/java/ghidra/graph/program/BlockGraphTaskTest.java
+++ b/Ghidra/Test/IntegrationTest/src/test/java/ghidra/graph/program/BlockGraphTaskTest.java
@@ -4,9 +4,9 @@
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
- * 
+ *
  *      http://www.apache.org/licenses/LICENSE-2.0
- * 
+ *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
@@ -22,6 +22,8 @@ import java.util.Map;
 import org.junit.Test;
 
 import ghidra.graph.*;
+import ghidra.graph.visualization.DefaultGraphDisplayProvider;
+import ghidra.program.model.address.AddressSet;
 import ghidra.program.model.block.CodeBlockModel;
 import ghidra.program.util.ProgramSelection;
 import ghidra.service.graph.*;
@@ -225,6 +227,36 @@ public class BlockGraphTaskTest extends AbstractBlockGraphTest {
 		assertNotNull(e3);
 		assertNotNull(e4);
 		assertNotNull(e5);
+	}
+
+	@Test
+	public void testAppendGraph() throws Exception {
+		String modelName = blockModelService.getActiveBlockModelName();
+		CodeBlockModel model = blockModelService.getNewModelByName(modelName, program, true);
+		ProgramSelection selection =
+			new ProgramSelection(new AddressSet(addr(0x1002200), addr(0x01002203)));
+		GraphDisplayProvider graphService = new DefaultGraphDisplayProvider();
+		runSwing(() -> graphService.initialize(tool, tool.getOptions("foo")));
+		BlockGraphTask task =
+			new BlockGraphTask(new BlockFlowGraphType(), false, false,
+				false, tool, selection, null, model, graphService);
+		task.monitoredRun(TaskMonitor.DUMMY);
+		waitForSwing();
+
+		GraphDisplay display = graphService.getActiveGraphDisplay();
+
+		AttributedGraph graph = display.getGraph();
+
+		assertEquals(2, graph.getVertexCount());
+
+		selection = new ProgramSelection(new AddressSet(addr(0x01002239)));
+		task = new BlockGraphTask(new BlockFlowGraphType(), false, true, true, tool, selection,
+			null, model, graphService);
+		task.monitoredRun(TaskMonitor.DUMMY);
+		waitForSwing();
+
+		graph = display.getGraph();
+		assertEquals(3, graph.getVertexCount());
 
 	}