Supporting running in the metro Richmond area
While it depends on the person, in my younger days I did as many as 3 races in a 24 hour period (all 10K or less). Ted Puolos in D.C has run as many as 230 races in a year and I think Chuck Engle did 50 marathons in 50 states in under 3:00:00 in 2006. I know that he has won marathons on successive days in the past.
A large measure of how well you race will be determined by your base, the amount and intensity of the training you do as well as the pace you race. Your body and finishing times will tell you if you need more rest between outings.