"Add tags" overwriting existing tags?

I am new to Hazel and have a little issue I can't seem to fix; I've searched the forums and don't see a similar question, but pardon me if this has been answered somewhere else.
I want to do this:
Modify a file name in a specific way by adding a bit of text to the name
Trigger Hazel to, when it sees that file name change, move this file with the modified name to a different folder, and then add a tag to the file.
Everything works...except that when these files already have existing tags, Hazel removes those existing tags before adding the new one I want it to add. So instead of "add tags," the action is more like "replace existing tags and add tags"
Any thoughts on how I might do what I intend for Hazel to do? Thanks.
I want to do this:
Modify a file name in a specific way by adding a bit of text to the name
Trigger Hazel to, when it sees that file name change, move this file with the modified name to a different folder, and then add a tag to the file.
Everything works...except that when these files already have existing tags, Hazel removes those existing tags before adding the new one I want it to add. So instead of "add tags," the action is more like "replace existing tags and add tags"
Any thoughts on how I might do what I intend for Hazel to do? Thanks.