Ternary and quaternary Heusler alloys have attracted attention in the last decade as advanced new alloys for environmentally-friendly high-efficiency solid state refrigeration in the vicinity of room temperature. To optimize their performance, a merged magnetic and crystallographic phase transformations is desired, as it results in a substantially larger change in entropy. The crystallographic phases (and their symmetry), as well as the nature of the magnetic phases (e.g. anti-ferromagnetic or spin glass), are also important in the determination of the entropy change and hence on their performance in magnetic refrigeration. We studied alloys of Ni-Mn-In and Ni-Mn-In-Co of various compositions. The alloys compositions were determined using Rutherford Backscattering Spectrometry (RBS). Synchrotron and neutron diffraction at different temperatures and under different magnetic fields were used to analyze the phases and phase transformations, as well as for determination of anti-ferromagnetic structure. The high temperature phase (austenite) of all alloys studied was found to be cubic L21; the martensitic phase varies greatly, between monoclinic (P 1 2/m 1), orthorhombic or tetragonal. The higher temperature magnetic phase of all studied alloys was ferromagnetic, while the low temperature phase was low-magnetization, anti-ferromagnetic for some alloys and spin glass for others. The best performance was demonstrated by alloys transitioning from cubic to monoclinic, simultaneously with ferromagnetic to spin glass transition.