Second, half-breeds exist. Magic-users can have children from giants, goblins, veela and, possibly, some other creatures. These half-breed can use magic, and there are two possibilities: they have MM genes or they have some m gene. m gene should be recessive gene, when appears with M gene, because according to HP wiki all known half-breeds can use magic. So half-breeds have MM or Mm genes.

Canon has Hagrid and Maxime (half-giant), Fleur and Gabrielle (one-quarter veela), and Filius Flitwick (part goblin). Veelas and goblins use forms of magic, but giants don't. That may be not because giants lack the genetic ability, but because they lack the attention or intelligence to learn how to make use of it, though. Goblins appear to have intelligence around human level, but use magic differently from witches and wizards.

Other species noted for using their own flavors of magic include house-elves and centaurs. There aren't any part-house-elf or part-centaur characters in canon or HPMoR, though.