For example, take Canis lupus, the species of dog and wolf. Within their species, can all dog and wolf types crossbreed? We can forget the logistics and assume this is all done through artificial insemination or in vitro methods (let's assume that the in vitro methods would be feasible).
If yes to the main question, does cross-breeding stop at the species class, or does cross-breeding extend across other taxonomic classes? From what I gathered, the taxonomic classes seem somewhat loose in their definitions. Perhaps I should ask, is there a rule "in general" to cross-breeding?
Let me know if this question ought to be refined in any way.