Summary: Very recently, the idea of studying structures equipped with two or more soft topologies has been considered by several researchers. Soft bitopological spaces were introduced and studied, in 2014, by B. M. Ittanagi [Int. J. Comput. Appl. 107, No. 7, 1–4 (2014; doi:10.5120/18760-0038)] as a soft counterpart of the notion of bitopological space. and, independently, in 2015, by M. Naz et al. [“Separation axioms in bi-soft topological spaces”, Preprint, arXiv:1509.00866]. In 2017, A. F. Hassan [Int. J. Comput. Appl. 176, No. 9, 26–30 (2019; doi:10.5120/ijca2017915573)] too introduced the concept of soft tritopological spaces and gave some first results. The notion of \(N\)-topological space related to ordinary topological spaces was instead introduced and studied, in 2011, by L. N. M. Tawfiq and R. N. Majeed [“\(N\)-topological space and its applications in artificial neural networks”, Ibn al-Haytham J. Pure & Appl. Sci. 24, No. 1, 1–11 (2011)]. In this paper we introduce the concept of Soft \(N\)-Topological Space as generalization both of the concepts of Soft Topological Space and \(N\)-Topological Space and we investigate such class of spaces and their basic properties with particular regard to their subspaces, the parameterized families of crisp topologies generated by them and some new separation axioms called \(N\)-wise soft \(T_0\), \(N\)-wise soft \(T_1\), and \(N\)-wise soft \(T_2\).