Diagram diagram1 = ...; // the already opened diagram
Diagram diagram2 = ...; // the additional diagram
diagram1.eResource().getContents().add(diagram2); // do it inside a feature/write transaction

Diagram diagram = ...; // the additional diagram

String path = "/project/file.diagrams";
ResourceSet resourceSet = new ResourceSetImpl();
Resource resource = resourceSet.getResource(URI.createPlatformResource(path, true));
resource.getContents().add(diagram);
try {
   resource.save(Collections.emptyMap());
} catch(IOException e) {
   e.printStackTrace();
   // e.g. log error
}