@Joe492 When I have guests checking in on the same day another set is checking out, I usually send a message stating the following;
1. We hope you have been enjoying your stay. (Usually personalized based on previous interaction with the guest)
2. Check-out is at X time.
3. We facilitate late check-out when possible, however we have guests checking in tomorrow at X time and we will need time to prepare for their arrival.
4. The house keeper will arrive at X time.
So far, I have never had guests who stay past check-out without my permission.