Topological insulators constitute a new phase of matter protected by symmetries. Time-reversal symmetry protects strong topological insulators of the Z(2) class, which possess an odd number of metallic surface states with dispersion of a Dirac cone. Topological crystalline insulators are merely protected by individual crystal symmetries and exist for an even number of Dirac cones. Here, we demonstrate that Bi-doping of Pb1-xSnxSe (111) epilayers induces a quantum phase transition from a topological crystalline insulator to a Z(2) topological insulator. This occurs because Bi-doping lifts the fourfold valley degeneracy and induces a gap at (Gamma) over bar, while the three Dirac cones at the (M) over bar points of the surface Brillouin zone remain intact. We interpret this new phase transition as caused by a lattice distortion. Our findings extend the topological phase diagram enormously and make strong topological insulators switchable by distortions or electric fields.