What configuration options are you missing in the HTML tile config?
There is no way to "clone" the built in HTML tile and then alter the config, alternatively you can mimic the HTML tile behaviour using a custom view tile.
It may be best to explain what is that you are trying to achieve, and then we can come up with the best route to take.
If you wanted to make a deployable asset that can be re-used across multiple places, you can see:
Creating Custom View Tiles and the Jive SDK:
jive-sdk create tile-app-simple
If I am understanding the nature of the question, this should allow for you to create multiple versions of a single HTML Tile.
Does that help?