1jimbo23
You absolutely can do this; however (and I don't know what part of the world you live in but I am assuming you are in the Northern hemisphere and are entering fall) this is the worst time to try and root cuttings. Plumeria are about to go dormant. A much better time would be in early spring.
Cut the three branches, leaving a 3 inch + stub on the plant; new branches will grow from these stubs eventually. Let the cuttings callous for a week to ten days, and then plant. Don't water until you see new leaves emerge, signifying root development.
Good luck!
