How can you prove in court that a tenant is breaking the lease by having extra people moving into the unit?
Do they live there or just stay sometimes?
Talk to the tenant and tell them that you are concerned there are people living there who are not on the lease and if that is the case, they are in violation of the lease and will need to move.
Otherwise, put up a security camera, do inspections of the home, do drivebys to check for cars.
This is why I put cameras, ring door bells and we have quartly site visits/ maintenance check up with our pest control provider to always have eyes on our asset. If tenant isn't keeping up with the unit they will be notified and if that issue is not address there lease will not be renewed.
Don't be a absent owner because the money is flowing in. Keep a eye on your asset at all times
You obviously know that's the case so just go ahead and send a Notice To Quit for Reason Other Than Non-Payment of Rent. It let's the tenant know that YOU KNOW they have violated the lease by having additional people stay at the property. Give them the required notice for the state (usually 3-5 days) to get in compliance or that you will proceed with eviction. Remind them that lease violations are not included in the eviction moratorium.
I bet once you give them written notice (post it to their door and take a photo of it; send it by registered mail with return receipt), they will take you and the situation serious. Don't speak to them - keep everything in writing - and don't engage in any of the "where's your proof." With any response, simply state they have 'X"days to cure the situation and nothing more. They will...