The thermodynamic stability of the premartensite (PM) phase has been a topic of extensive investigation in shape memory alloys as it affects the main martensite phase transition and the related physical properties. In general, the PM phase is stable over a rather narrow temperature-composition range. We present here evidence for chemical pressure induced suppression of the main martensite transition and stabilization of the PM phase over a very wide temperature range from 300 to ∼5K in a magnetic shape memory alloy (MSMA), Ni50Mn34In16, using magnetic susceptibility, synchrotron x-ray powder diffraction (SXRPD) studies, and first-principles calculations. The ac-susceptibility studies show a highly skewed and smeared peak around 300 K without any further transition up to the lowest temperature of our measurement (5 K) for ∼5% Al substitution. The temperature evolution of the SXRPD patterns confirms the appearance of the PM phase related satellite peaks at T≤300K without any splitting of the main austenite (220) peak showing preserved cubic symmetry. This is in marked contrast to the temperature evolution of the SXRPD patterns of the martensite phase of the Al free as well as ∼3% Al substituted compositions where the austenite (220) peak shows a clear splitting due to Bain distortion signalling symmetry breaking transition. Our theoretical calculations support the experimental findings and reveal that the substitution at the In site by a smaller size atom, like Al, can stabilize the PM phase with preserved cubic symmetry. Our results demonstrate that Al-substituted Ni-Mn-In MSMAs provide an ideal platform for investigating the physics of various phenomena related to the PM state.