I've only read one thread where it went to hell, and that's where the breeder would not let the co-owner (person that had the bitch) breed with any other dog in the whole of Australia ie every suggested pairing was rejected by the original breeder. Not good.
Personally I don't like sharing and the risks that go with that. But you need to have a written agreement and be really clear about what you expect. With horses - Owners often lease out their horses if they want someone else to pay for the horses upkeep but return the horse if they don't want it any more. It usually doesn't cost anything to get the lease of the horse - because they cost so much to keep. But with cars - it does. That might be a contract that works better than co-ownership. Tho with racehorses they have co-ownership or shares. Maybe those sorts of contracts would work.