There is no raison d'etre for (and no socially redeeming value of, and no easy way of producing) a 120/208 volt system that is not from a symmetric wye configuration.
The reason 208 volts became accepted as a standard is because it is the natural result of configuring a return conductor to have 120 volts potential from each of the 3 legs of a 3 phase system. It combines the advantages of 3 phases with the advantages of 240 volts over 120 volts (fewer or thinner conductors needed), although some appliances come in slightly different versions for 208 versus 240 volts.
Also the high leg, or stinger, is the natural result of configuring a return conductor having 120 volts potential from each of two legs of a 240 volt 3 phase system so as to provide a 120/240 volt feed (or subfeed).