An invitation to "Avis First" status is supposed to occur after 12 rentals (rolling 12-month period instead of calendar year). I just called, and they do not do status matches. (I'd love to be contradicted on this one! But that's what one person told me.)
The main reasons I looked into this were: 1) a promo I saw for Avis First people which will get you a two-day weekend rental after three rentals and 2) the fact that they have the Hyundai Sonata. Finally some cars that will draw me away from Hertz and their Toyotas (and the occasional Nissan 350Z

).