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We explore an opportunity to induce and control tetragonal distortion in materials using the ideas of Bain transformation path for multiatomic systems with body– and face-centered symmetries. The concept is illustrated in the case of FeNi_1-xCo_x magnetic alloy formed by substitutional doping of the L10 FeNi magnet with Co. Using electronic structure calculations we demonstrate that the tetragonal strain in this system can be controlled by concentration and it reaches maximum around x = 0.5. This finding is then applied to create a large magnetocrystalline anisotropy in FeNi_1-xCo_x system. We demonstrate that this anisotropy can be significantly improved by delicate tuning the tetragonal distortion, electronic concentration and chemical anisotropy. We discuss possible experimental ways to create such magnet.