Change the terms of the current lease or sign a new one

  The law varies from state to state, so the first thing you need to do is to read the lease and all accompanying documents carefully. For example in the state of New Jersey you can read the following.

  NO GUEST OF THE TENANT MAY OCCUPY THE DEMISED PREMISES FOR MORE THAN 10 DAYS IN A TWELVE MONTH PERIOD UNLESS A TENANCY APPLICATION IS FILLED WITH THE LANDLORD AND ACCEPTED BY THE LANDLORD. OCCUPANCY BY A GUEST BEYOND THE ABOVE PERIOD SHALL CONSTITUTE A BREACH OF THE LANDLORD'S RULES AND REGULATIONS.

  That line basically means that you occupied the premises unlawfully giving you literally no rights. However, as you stated the owner was aware about the situation which tells me that probably the best solution would be to talk to the owner and decide the course of actions either adding you lawfully to the list of tenants or probably signing another lease with the owner after the apartment is surrendered accordingly to the terms of the previous lease. In any case, if you still want to occupy this apartment you better pay the rent.