The phrase "cross breeding" refers to the practice of breeding animals or plants from different breeds or species to create offspring with desired traits. Full definition
The breed began cross breeding with others as they became good cattle drivers. (petpremium.com)
It is generally true that studies have shown greater longevity in cross bred dogs. (thehappypuppysite.com)
The resulting offspring have become very popular in some cases with puppy seekers deliberately choosing to have one of these designer cross breed puppies. (dogbreedhealth.com)