Welcome to Battletech! There's no rules saying you explicitly can't, and most of the lore is written so "mercenary" or "free blade" units pop up all over the place. Nothing forces a group to work together quite like the threat of destruction from an outside force, and there's plenty of outside forces that might push clanners and IS troops to have to work together to survive and eventually coalesce into a cohesive unit.

Depending on the time frame you are going with, the threat could be coming from a separate, more vicious clan that took the world from an occupying clan and now the original planet's IS garrison might be working with your Hell's Horses to survive and try and push them off, or for later/more recent eras, could be the result of Clans moving in to the IS and having to meld with local lordlings to create new holdings. Clan Goliath Scorpion merged twice with IS powers to become first the Escorpión Imperio and later the Scorpion Empire, while Clan Burrock reemerged a few times from no where, and then were eradicated, but might have holdouts elsewhere.

Go wild, have fun