I had the same situation. I have a Sterling All-Terrain towbar that I used with crossbar on my old Chevy Tracker with Roadmaster baseplate. Then I bought a slightly used new to me tow car that already had a Blue Ox baseplate installed.
Yes, I ditched the crossbar and just swapped out the ends of the Sterling towbar with adapter ends that would match the Blue Ox connections on the car.
2002 Itasca Suncruiser 32V
2012 Suzuki Grand Vitara