A "half stage" is a rocket stage which separates with its engines, but not fuel tanks. Common examples include Atlas (1.5 stages), Atlas-Agena (2.5 stages), and Atlas-Centaur (2.5 stages).
On paper, one could create a "one-and-two-half-stage" rocket. It burns for a while, then drops some engines. Then it burns some more, and drops more engines. It then burns its remaining engines to orbit.
Alternately, a "two-and-two-half-stage" rocket is also theoretically possible. It burns for a while, drops some engines, burns some more, and drops its lower stage. The upper stage burns for a while, drops some engines, and then finished its burn to orbit.
I'm sure such a design would have numerous disadvantages (feel free to point them out in the comments). However, are there any advantages over other designs?