Strained coherent film growth is commonly either limited to ultrathin films or low strains. Here, we present an approach to achieve high strains in thicker films, by using materials with inherent structural instabilities. As an example, 50 nm thick epitaxial films of the Fe70Pd30 magnetic shape memory alloy are examined. Strained coherent growth on various substrates allows us to adjust the tetragonal distortion from c/a{bct}=1.09 to 1.39, covering most of the Bain transformation path from fcc to bcc crystal structure. Magnetometry and x-ray circular dichroism measurements show that the Curie temperature, orbital magnetic moment, and magnetocrystalline anisotropy change over broad ranges.