YES, YOU CAN!!
There are many registries within our country that allow you to register and compete with your rescue/mixed breed dog. You would need to apply for an Indefinite Listing Privilege or in some cases Listing Privilege with each registery. Some registeries elect to just include purebreds (or what you are pretty sure is a purebred) while others let both types of dogs be registered. You can compete in obedience, tracking, flyball and agility. All of the registries shown below do require that your dog be spayed or neutered. Check it out and then go start training!
American Kennel Club
Australian Shepherd Club of America
Mixed Breed Dog Clubs of American
American Mixed Breed Obedience Registration
United Kennel Club
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