I have done this a couple of times, in different situations, but always with the same car class.

One time, my flight reported delayed by several hours as I was driving to the airport. Since I was only a 2 hour drive from home, I pulled off the road, canceled my return flight, then made a new reservation in the National app. When I got to the airport I asked if I could just keep the same car and the agent said "Sure, one less to clean".

We did a driving vacation one time, and I needed to use a combination of 1-2-free days, regular free days, and paid days. Made reservations for a one-way from Detroit to Philadelphia, another one-way from Philly to Syracuse, and a 3rd one-way from Syracuse to Detroit. Each was an airport location, and each let me keep the same car - so Detroit got back the same car that I took.

Did almost the same thing with a PDX-LAS, LAS-LAS, and LAS-PDX - again, with no problem. I just told them at the return line that I wanted to keep the same car, so they had me pull off to the side while I went and talked to the counter.

Which is all to say - should be doable.