Simultaneous type A NN-fold supersymmetry with two different values of NN

We investigate one-dimensional quantum mechanical systems which have type A NN-fold supersymmetry with two different values of NN simultaneously. We find that there are essentially four inequivalent models possessing the property, one is conformal, two of them are hyperbolic (trigonometric) including Rosen–Morse type, and the other is elliptic.