We have calculated structural energy differences, magnetic interaction constants and mixing energies of Fe-Co-Ga(Zn) alloys in order to gain information about their suitability for ferromagnetic shape memory devices. We considered the classical Heusler structure as well as an ordering type in which the Co and one Fe sublattice are interchanged. The results of our density functional theory investigations suggest high Curie and martensitic phase transition temperatures for the Ga-based as well as for the Zn-based systems. In case of hypothetical Fe2CoZn alloys, the classically ordered Heusler structure is energetically preferred. In Ga based alloys, the ordering type with Co partially on Fe sites appears to be more stable. We propose that a systematic variation of composition by successive addition of Zn and Co to Fe-Co-Ga may result in a promising new ferromagnetic shape memory alloy of type Fe2−xCo1+xGa1−yZny.