So, Carnot engine is THE reversible engine operating on two reservoirs. No other engine can beat its efficiency on two reservoirs (eg. Otto cycle is not Carnot as it requires infinite number of reservoirs to pass through the isochoric step). It strikes me, however, that steps of a Carnot cycle are unique for every working substance that are considered in undergraduate thermal physics courses (rubber bands, ideal/vdW gases, extended wires).
Do there exist thermodynamic systems where there is more than one possible reversible cycle between two reservoirs? In other words, is there a system in which apart from a cycle which roughly corresponds to typical isothermal-adiabatic-isothermal-adiabatic (possibly with other state variables involved) there is some other way of performing a Carnot cycle?