I did switch cars last fall while renting from Hertz in Germany after a couple of days because I did not like what they had given me at the airport, and had no issues.

I did call ahead to a couple of local stations and airport near to where I was staying and got a switch arranged with no questions asked. Calling ahead would make sense if you want something specific to make sure they have it, or can arrange.

I got a new contract and rate but they honored the CDP I used on the original contract. I am a 5* member, and speak German, which may have helped.

Cheers,