Budget - Overlapping Rentals in Two Different Cities

I'm referring to having a car still out to my name in one city when I pick up a car in another city.

Is there any potential problem with this?

I ask this because it's cheaper (by a good bit) for me to keep my rental in city A while traveling to city B for a couple of days than returning my car in city A while in City B and then getting a new rental when I return to City A.

Had a two week budget rental in PDX. During that period, had to fly to Boston, so made a reservation for a short budget rental at the Boston airport, but keeping my PDX rental for my return. When I got to Boston and went to check in (for some odd reason, I didn't use fastbreak), the desk noticed I had an outstanding rental. They said I couldn't have two budget car rentals at the same time. I argued with them, etc., and they relented. So you might want to "clear the waters" in advance...

My husband and I used our one family COSTCO card to make two reservations at the same time with Budget -- in two different cities. I was travelling first and had no problem. But when my husband tried to rent the car in the second city, they said no! Even though they were under two different name. I couldn't believe it!

Go with another company perhaps?