Exploring alternatives to the Cu2ZnSnS4 kesterite solar cell absorber, we have calculated first principle enthalpies of different plausible structural models (kesterite, stannite, P4¯ and GeSb type) for Cu2FeSnS4 and Cu2MnSnS4 to identify low and high pressure phases. Due to the magnetic nature of Fe and Mn atoms we included a ferromagnetic (FM) and anti-ferromagnetic (AM) phase for each structural model. For Cu2FeSnS4 we predict the following transitions: P4¯ (AM) −→−−−−16.3GPa GeSb type (AM) −→−−−−23.0GPa GeSb type (FM). At the first transition the electronic structure changes from semi-conducting to metallic and remains metallic throughout the second transition. For Cu2MnSnS4, we predict a direct AM (kesterite) to FM (GeSb-type) transitions at somewhat lower pressure (12.1 GPa). The GeSb-type structure also shows metallic behaviour.