"Lay down and roll over" are commonly used commands for dogs in training. These commands are essential in building obedience, discipline, and basic skills for dogs. However, if you're looking to give your furry friend a more sophisticated command, here are some synonyms that can be used interchangeably: "Downward dog," "Lie flat," "Climb down and turn," "Prostrate," "Lie still and revolve." These commands are not only great alternatives but can also add some fun and excitement to your dog training sessions. It's always good to mix things up and keep your dog's attention focused on you.