I've had the equivalent of two free nights on an eight night stay with fourth night free, although I forget whether it was six nights total with third night free or eight nights with fourth night free. My impression is that this is generally allowed, although you don't get additional once per stay amenities even if you book two back to back stays.

Don't forget the FHR requirement to pay with an AmEx card in the same name as the reservation. If you also want elite credit in some hotel frequent guest program, usually the requirement is that both the name on the reservation and the name on the credit card must be the person who actually stays and the same person on the hotel program account, so be careful about what credit card is used and what name is on the hotel folio.