It is a fact (to the best of my knowledge) that for optimum thrust from a rocket engine, one of the most important factor is the design of its converging/diverging Nozzle - the diverging cone to be very specific. This design should be able to provide "ideal expansion" of the exhaust gases i.e. nozzle exit pressure being equal to atmospheric pressure.
Since the atmospheric pressure will keep reducing as the rocket ascends, will it not be advantageous to have many more stages (say one stage for every 25 km), so that nozzles for each stage can be designed to match the atmospheric pressure at a given altitude?
Further; perhaps an "adjustable" profile of nozzle (w.r.t. altitude) would be the best, if possible. Has such an attempt been made?