High entropy shape memory alloys (HE-SMAs) show reversible martensitic phase transformations at elevated temperatures. HE-SMAs were derived from binary NiTi, to which the elements Cu, Pd, Zr and Hf are added. They represent ordered complex solid solutions. Their high temperature phase is of B2 type, where the added elements occupy sites in the Ni-(Cu, Pd) and Ti-sub-lattices (Zr, Hf). In the present study, advanced microstructural and thermal characterization methods were used to study the effects of the additional alloy elements on microstructures and phase transformations. The ratios of Ni-equivalent (Ni, Cu, Pd) and Ti-equivalent (Ti, Zr, Hf) elements in HE-SMAs were varied to establish systems that correspond to stoichiometric, under- and over-stoichiometric binary alloys. It is shown that basic microstructural features of cast and heat-treated HE-SMAs are inherited from the nine binary X–Y subsystems (X: Ni, Cu, Pd; Y: Ti, Zr, Hf). The phase transition temperatures that characterize the martensitic forward and reverse transformations depend on the concentrations of all alloy elements. The data obtained demonstrate how martensite start temperatures are affected by deviations from the composition of an ideal stoichiometric B2 phase. The findings are discussed in the light of previous work on the concentration dependence of SMA transformation temperatures, and directions for the development of new shape memory alloy compositions are proposed. © 2020 The Authors