Both a Standard SUV (SFAR) and a Premium Elite SUV (UFAR) are typically 5-passenger vehicles. It's unlikely either of those will have enough room for four large suitcases. Alamo's example make/model for the SFAR class is Ford Edge and for a UFAR it's a BMW X3, neither of which can probably fit 4 large suitcases in the rear luggage area. You'd probably want to look at a Premium Crossover (PGAR) or 7-passenger SUV (FFAR), or even a Minivan (most space).

Note that a Ford Explorer (7-passenger) would be considered an RFAR at Avis/Budget and an FRAR at Hertz/Dollar/Thrifty whereas a Ford Expedition or similar with all companies would be an FFAR.