I typically rent from Hertz and rent quite a lot from them. I have a "president's gold" membership or something that I was sort of grandfathered into by my company's corporate account a few years back. One of the perks is an auto upgrade to a class or two above what you're reservation is, so that typically means if you have a midsize reserved they'll let you take an Infiniti or a Nissan Maxima or a decent SUV like a Durango/Tahoe for no upcharge.

I have also rented several times from Alamo/National (same company). I signed up for the Emerald Rewards program for free, and that also includes an automatic upgrade. I've also found that picking up on a Thursday helps them be pretty flexible on what they let you pick since the weekend rush hasn't set in yet. I rented a 2011 Hyundai Sonota from Alamo because it was the nicest they had one time - I was so impressed by that car I would honestly look for one intentionally in the future (leather, XM, bluetooth, moonroof, good power AND 35mpg freeway!).

As always though, these are all dependent on your local conditions, how nice people are to and you to them, seasonal/trending travel flow, etc. YMMV

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2001 X5 4.4i
2002 Honda S2000