Finding a systematic construction for integrable partial differential systems in four independent variables is a long-standing problem in modern theory of integrable systems. In this talk we address the problem in question by presenting a broad new class of (3+1)-dimensional dispersionless integrable systems possessing nonisospectral Lax pairs written in terms of contact vector fields; please see arXiv:1401.2122 (to appear in Lett. Math. Phys. (2017)) for details.