How many tunable parameters to attain a spin degeneracy between Landau levels?

The spin degeneracy of Landau levels is generically lifted by the Zeeman interaction, and also by the spin-orbit coupling in non-centrosymmetric solids. In the absence of any crystalline point-group symmetry, such a spin degeneracy can only be found by tuning three real parameters; we have exhaustively identified all symmetry classes of solids for which this number is reduced from three. In particular, only one parameter is needed in the presence of rotational symmetry; this parameter may be the magnitude or orientation of the field, or the bias voltage in tunneling spectroscopy. Signatures of single-parameter tunability include: (i) a smooth crossover between period-doubled and -undoubled quantum oscillations in the low-temperature Schubnikov-de Haas effect, and (ii) "magic angle" magnetoresistance oscillations. Case study is discussed for the Rashba-Dresselhaus two-dimensional electron gas subject to an arbitrarily oriented magnetic field.