Treat, deal, handle are comparable when they mean to have to do with a person or thing in a way specified in the context.
Treat in the sense of doing about, serving, or coping with is usually accompanied by context indicating an attitude, temperament, or point of view determining behavior or a manner of approach or execution.
Deal , followed by with , may suggest managing, controlling, or authoritative disposing and sometimes it suggests a relationship between persons or parties on a more or less even basis.
Handle is often interchangeable with treat and deal (with); it may suggest a placing, directing, disposing, or manipulating with or as if with the hand.