N-fold parasupersymmetry

We find a new type of nonlinear supersymmetries, called N-fold parasupersymmetry, which is a generalization of both N-fold supersymmetry and parasupersymmetry. We provide a general formulation of this new symmetry and then construct a second-order N-fold parasupersymmetric quantum system where all the components of N-fold parasupercharges are given by type A N-fold supercharges. We show that this system exactly reduces to the Rubakov-Spiridonov model when N = 1 and admits a generalized type C 2N-fold superalgebra. We conjecture the existence of other "N-fold generalizations" such as N-fold fractional supersymmetry, N-fold orthosupersymmetry, and so on.