Partially Recoverable Second Stage

Even though, I am not a fan of recovering the second stage of a rocket. For some LEO missions this approach is feasible. The main objective of my idea is to recover the essential parts of a rocket stage, the engines. In order to achieve this goal, I propose a rocket second stage with two separate propellant tank groups (fuel and the oxidizer tanks form a group). The one, close to the engines would be small and consumed during recovery. The much bigger second group of tanks would be used to put the payload into orbit.

Once the payload is deployed to the orbit, the second stage would separate into two. The heavy propellant tanks at the top would be discarded to crash on an ocean. The section containing the engines and a small propellant tank group would slow down and land on a recovery platform offshore. Much reduced weight would require less fuel for recovery. Additionally, much smaller size would be easier to control during landing compared to a tall and thin structure. At the end, most valuable parts of a rocket, the engines are recovered and the discarded tank could be easily replaced with minimal cost.