  We explore an opportunity to induce and control tetragonal distortion in
materials. The idea involves formation of a binary alloy from parent compounds
having body-centered and face-centered symmetries. The concept is illustrated
in the case of FeNi$_{1-x}$Co$_x$ magnetic alloy formed by substitutional
doping of the L1$_0$ 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 for $x=0.5$. This finding is
then applied to create a large magnetocrystalline anisotropy (MAE) in
FeNi$_{1-x}$Co$_x$ system by considering an interplay of the tetragonal
distortion with electronic concentration and chemical anisotropy. In
particular, we identify a new ordered FeNi$_{0.5}$Co$_{0.5}$ system with MAE
larger by a factor 4.5 from the L1$_0$ FeNi magnet.
