Iron-based shape memory alloys are promising candidates for large-scale structural applications due to their cost efficiency and the possibility of using conventional processing routes from the steel industry. However, recently developed alloy systems like Fe–Mn–Al–Ni suffer from low recoverability if the grains do not completely cover the sample cross-section. To overcome this issue, here we show that small amounts of titanium added to Fe–Mn–Al–Ni significantly enhance abnormal grain growth due to a considerable refinement of the subgrain sizes, whereas small amounts of chromium lead to a strong inhibition of abnormal grain growth. By tailoring and promoting abnormal grain growth it is possible to obtain very large single crystalline bars. We expect that the findings of the present study regarding the elementary mechanisms of abnormal grain growth and the role of chemical composition can be applied to tailor other alloy systems with similar microstructural features.