Month to Month Apartment Rentals. Portland Month to Month Apartment Rentals. Thanks for choosing ASI! At Alternative Suites International, we are proud to provide an amazing selection of month to month apartments for rent in Portland. There are many reason why one might want a month to month lease on an apartment in Portland. Business travelers, individuals or families on extended vacations, or anyone considering a permanent relocation, could all find a need for a month to month apartment.