Yes, you can. As they are the same species then they can be bred together. Think of it like dogs- a labrador can be mixed with a poodle, as although they are diffenet breed they are the same SPECIES
English Grey Partridge is a rare breed and is very much in season until spring, very good for turning a profit with restaurants. Pheasant is also another profit breed.
If you really mean breeds, there are none - breeds are true-breeeding man-made strains of a domesticated animal.
If you mean species, that depends on what you really count as quail as the common...
There aren't any breeds, only species, but if you are new to keeping/breeding them, Jap' quail (coturnix japonica, domesticated), are simplest - pick a colour that you like that is easy to sex - NOT...