There are up to 90 apartments per building at the moment. If it fills up then you have to find another building. The apartments are a good choice for those taking breaks as they do not have a timer looming over them and unlike private rooms, they do not have a 3rd party in control of you losing them. As big FCs tend to churn through members, taking a long break would likely make you a target for dismissal at which point you'll have a limited time to collect your things from the Resident Caretaker npc before the server eats them. Apartments will of course be limited in that they each belong to the character and not your account so visiting your alts apartments will treat you as a guest.