Exploration of new ferroic (ferroelectric, ferromagnetic or ferroelastic) materials continues to be a central theme in condensed matter physics and to drive advances in key areas of technology. Here, using thin-film composition spreads, we have mapped the functional phase diagram of the Ni-Mn-Ga system whose Heusler composition Ni(2)MnGa is a well known ferromagnetic shape-memory alloy. A characterization technique that allows detection of martensitic transitions by visual inspection was combined with quantitative magnetization mapping using scanning SQUID (superconducting quantum interference device) microscopy. We find that a large, previously unexplored region outside the Heusler composition contains reversible martensites that are also ferromagnetic. A clear relationship between magnetization and the martensitic transition temperature is observed, revealing a strong thermodynamical coupling between magnetism and martensitic instability across a large fraction of the phase diagram.