We have performed a quantum-mechanical study of a series of stoichiometric Ni2MnSn structures focusing on pressure-induced changes in their magnetic properties. Motivated by the facts that (i) our calculations give the total magnetic moment of the defect-free stoichiometric Ni2MnSn higher than our experimental value by 12.8% and (ii) the magnetic state is predicted to be more sensitive to hydrostatic pressures than seen in our measurements, our study focused on the role of point defects, in particular Mn-Ni, Mn-Sn and Ni-Sn swaps in the stoichiometric Ni2MnSn. For most defect types we also compared states with both ferromagnetic (FM) and anti-ferromagnetic (AFM) coupling between (i) the swapped Mn atoms and (ii) those on the Mn sublattice. Our calculations show that the swapped Mn atoms can lead to magnetic moments nearly twice smaller than those in the defect-free Ni2MnSn. Further, the defect-containing states exhibit pressure-induced changes up to three times larger but also smaller than those in the defect-free Ni2MnSn. Importantly, we find both qualitative and quantitative differences in the pressure-induced changes of magnetic moments of individual atoms even for the same global magnetic state. Lastly, despite of the fact that the FM-coupled and AFM-coupled states have often very similar formation energies (the differences only amount to a few meV per atom), their structural and magnetic properties can be very different.