Yes we always started just the two inboard engines prior to push back and the outers when the push back was complete. This was for a number of reasons, but I do seem to remember it was not unheard of to break the tow bar shear pin on the initial push, so the less power the better
Remember that Concorde had no APU and no across the ship ducting for stating engines, therefore prior to push an air start unit was plugged into each pair of engines and the inboard engines would be started. This allowed, after push back, air from each inboard engine to be used to start it's outboard engine.
The other good reason for starting the inboards prior to push was that with no APU the cabin temp would rise quite quickly [specially in places like Bahrain in summer] and never mind the passengers
comfort, but some of M2dude and ChristiaanJ fancy electronic equipment was very temp sensitive , especially those intake control units down the rear galley. With Two engines running we could use their bleed air to at least try and hold the cabin air temp during the push back
When we first started LHR-IAD flights[ prior to thin lip///54% and other mods which improved our range] some thought was given to towing the aircraft to the taxi way near the end of the runway before starting engines so as to save fuel. I do not remember this actually ever being done though.
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