The question Would there be any advantages for a rocket with two “half stages”? begins with:
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).
Atlas is a family of American missiles and space launch vehicles. The original Atlas missile was designed in the late 1950s and produced by the Convair Division of General Dynamics, to be used as an intercontinental ballistic missile (ICBM). It was a liquid propellant rocket burning liquid oxygen and RP-1 fuel in three engines configured in an unusual "stage-and-a-half" or "Parallel Staging" design: its two outboard booster engines were jettisoned during ascent, while its center sustainer engine, propellant tanks and other structural elements were retained through orbital insertion (for orbital flights).
Other weight-saving techniques used in some designs included leaving off the paint and making the wall so thin it needed to be inflated with pressurized nitrogen when not fully fueled and pressurized to avoid collapse.
How much mass was dropped, at what point in the flight, and how much did engine-mass-dropping increase maximum payload mass to LEO?