We show that the nonlinear chiral supermultiplet allows one to construct, over given two-dimensional bosonic mechanics, the family of two-dimensional N = 4 supersymmetric mechanics parameterized with the holomorphic function λ(z). We show, that this family includes, as a particular case, the N = 4 superextensions of twodimensional mechanics with magnetic fields, which have factorizable Schroedi...