An all liquid alternative to solid augmentation.
The hot staging ring--an erstwhile "temporary" bodge, is true dead weight --but a ring used for nastier combustion products might pay for itself mass-wise if it also serves as tankage for nasty propellants.
Further--perhaps a largely spent ring could also double as a thrust reverser to allow a cooler interface between the first and second stages.
Once stage separation is done, the ring falls away like SH's hot stage ring--and the first stage can land with cleaner Methalox engines--all the heat and/or coking damage happens only to something that you were going to cast off anyway.
Space Freighter being in-line was to have something along the lines of a hot staging ring/join...though a parallel staged Space Freighter may not have needed ANY such ring--or used what I described to at least get a bit of Air- breathing without the whole airframe having to look like a chisel.
Two-Stage-and-a-Half to Orbit
Both winged--belly to belly, no Boostback burn.