Haven't tried it myself, but like Squid said, just edit the one you want to duplicate and change its name and whatever settings you need to be different. The docker template and the docker container both get whatever name you give it so if the name is different, you have a different one to run. I doubt the original will be removed or even stopped, but even if it is, you can just reload it from its template.
Try it and let us know if it works for you.