Yes, you can. "Breeds" are just pre-made genetics. Which means that all animals of a same breed have the exact same shape, so not crossing them would just look boring.
That said, not all breeds can be made in the Sims 3, as the game can't handle short legs. So you can't really have dachshunds that look like dachshunds, unless if you don't mind dachshunds with long legs.