Application of trans-stage for a recoverable rocket?

In message
David Spain wrote:

In this scenario, a smaller trans-stage is attached to the top

There are a couple of advantages to this approach:

1) The entire propellant load of the first stages could be used for ascent.

Not an advantage. You still need a similar amount of fuel for the
landing, all you've done is add extra tanks to hold it, increasing the
mass, and added more engines, also increasing the mass.

2) Simplification of the recovery effort of a multi-booster
configuration such as the Falcon-9 Heavy. Instead of having to manage
the recovery of three separate boosters, you only need deploy landing
legs on the three and have a single point-of-control for the active
recovery.

What are you proposing to use to hold the stages together, very long
bits of string? Consider why this wouldn't have worked to recover the
shuttle ET and SRBs as a single package...

Anthony