We consider a parametric nonlinear, nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian (with p > 2) and a Laplacian (a two phase equation). The reaction consists of a parametric ( p - 1)-superlinear term and a ( p - 1)-sublinear perturbation. We show that for all. > 0 big, the problem has at least three nontrivial smooth solutions, all with sign information. Also we determine their asymptotic behaviour as the parameter..8. When we strengthen the regularity of the perturbation term, we produce a second nodal solution, for a total of four solutions, all with sign information.