Domestic Medium Hair is a coat description, not a breed. It's the label used for mixed-ancestry cats whose fur falls between short and long: fluffier than a domestic shorthair, often with a plumed tail, tufts between the toes and a soft undercoat, but without a heavy ruff. They come in every color and pattern, from tabby and tuxedo to calico and solid black.
Because the ancestry is mixed, size, personality and health follow the cat rather than a breed standard. Most weigh 6 to 14 pounds and live 12 to 18 years. In St. Joseph, where the seasons swing from freezing nights to warm summers, the undercoat is worth planning around: expect extra brushing in spring and fall, and meet the cat before deciding, since temperament is the best guide.