> Rockets are usually two-staged + satellites.
I think that only applies to liquid fueled rockets. At a minimum the Scout family of rockets (USA) and the Lambda 4s (Japan) both use 4 stages. That is what I was trying to say above. The sibling comment also points out that you at least need a third stage to circularize the orbit, since you can't re-light solid rocket motors. I'm not exactly clear on why its 4 and not 3, but that seems to be the standard with solid fueled rockets.
I think it's for maneuvering. At least L-4S seemed to have had 3rd for the pitchover and 4th for the apogee kick. The first two were spin stabilized and unguided for political reasons. "Payload" stages built more like satellites are better suited for precise guidance.
(ISAS side of Japanese space programs is chock full of political BS, everything from the pencil rocket that continued on from IJN rocket researches to the "unguided" L-4S to the LUNAR-A probe with diameter of approximately 152-155mm to one-man laptop launchable Epsilon LV concept focusing on "civilian low-cost rapid launch demands")