  We construct the all loop effective action representing, for small couplings,
simultaneously self and mutually interacting current algebra CFTs realized by
WZW models. This non-trivially generalizes our previous works where such
interactions were, at the linear level, not simultaneously present. For the two
coupling case we prove integrability and calculate the coupled RG flow
equations. We also consider non-Abelian T-duality type limits. Our models
provide concrete realisations of integrable flows between exact CFTs and
exhibit several new features which we discuss in detail.
