Bit of a hypothetical question requiring a judgemental response!
My short answer would be not much more than the certified limits - at least not without significant modifications.
FL680 was achieved at the end of a zoom climb, so the Mach No was a lot less than 2.0
M2.23 was in a shallow dive. The object was to demonstrate sufficient margin to avoid surge following the worst temperature transient specified in the TSS regulations. To that end both the intake laws and engine operating lines were tweaked as functions of Mach No to minimise intake flow distortions and maximise surge margin. The result was a long way from the performance optimum one would need for steady cruise.
The power plant was being pushed to its limits at this Mach No.
(As an aside, the subsonic rules make no mention of temperature transients as a cause of Mach exceedences. Some recent incidents suggest this could usefully be reviewed)
The altitude limit could perhaps be more readily expamded. The aircraft normally flew a cruise climb bcause at Concorde cruising altitudes there was no ATC conflict. The altitude was very sensitive to ambient temperature and aircraft weight. FL600 would be associated with end of cruise on a coolish day.
To usefully increase cruise altitude would require more engine thrust, but this could only be obtained by increasing engine TET which would screw the engine fatigue life.
Increasing Mmo from 2.04 would need an increase in Tmo (400 deg K) at any temperature above (from memory) ISA. This in turn would affect the airframe fatigue life unless the structural material were changed. Even then, there were a lot of nonmetallic bits (seals etc) that would also have needed replacement.
Sorry if this is a gloomy assessment, but that is the way I see it!