While you could technically use "more versatile" and "most versatile", it's not considered grammatically incorrect, it sounds a bit awkward and is not the preferred way to express the idea.
Here are some better alternatives:
Comparative:
* More adaptable
* More flexible
* More multi-faceted
* More resourceful
* More all-around
Superlative:
* Most adaptable
* Most flexible
* Most multi-faceted
* Most resourceful
* Most all-around
Choose the option that best fits the specific context you're writing in.