My dog has two full sets of teeth both bottom and top rows. The vet actually pointed that out although we had noticed. She just never lost her "baby" teeth and the others grew in front of them

I also had extra teeth, but they came in sequentially and pushed the pre-existing teeth out. I had 3 sets of canines and first molars.

However, what the OP is talking about is a bit different. It sounds like the second set is set back in the palate a bit.