On the basis of previous work in Nordstr¨om & Malan (2024), we develop a new energystable scheme for incompressible multi-phase flows. In particular, we extend our previous work to introduce a multi-phase flow formulation with general interface regularization that complies with the previously developed stable baseline formulation and does not compromise energy stability. This extension can be used for all phase field (diffuse interface) models for which the phase advection equation is in conservative form.