I am assuming the lease he signed specifically states who resides there, correct (i.e., him)? You can, as you stated above, let him know you have become aware of additional occupants residing there with, it appears, his approval. If you wish to continue receiving rent from this group the person whose name is on the lease can then provide the additional funds to run background checks on these folks and if approved by you, begin paying the higher rent for each.
If he balks, I would not simply let him break the lease as you have indicated these folks seem to have begun to damage your rental property. Who (besides you) would pay for this if you simply let him break the lease without penalty?
Gail