The essence of the separate Universe approach, which has been widely used in cosmology, is to rephrase an inhomogeneous Universe with glued numerous homogeneous local patches. We show that the separate Universe approach can be generically used, as long as a theory under consideration is local and preserves the spatial diffeomorphism invariance. Remarkably, the separate Universe approach and subsequently the $¥delta N$ formalism can also apply to a Universe with large scale anisotropic pressure and also to modified theories of gravity, accepting a violation of Lorentz invariance. We also show that the same condition ensures the approximate existence of Weinberg’s adiabatic mode, the constant solution of the curvature perturbation.