Ba(Fe1-xCox)2As2 is the most tunable of the Fe-based superconductors (FBS) in terms of acceptance of high densities of self-assembled and artificially introduced pinning centres which are effective in significantly increasing the critical current density, Jc. Moreover, FBS are very sensitive to strain, which induces an important enhancement in critical temperature, Tc, of the material. In this paper we demonstrate that strain induced by the substrate can further improve Jc of both single and multilayer films by more than that expected simply due to the increase in Tc. The multilayer deposition of Ba(Fe1-xCox)2As2 on CaF2 increases the pinning force density (Fp = Jc × µ0H) by more than 60% compared to a single layer film, reaching a maximum of 84 GN/m3 at 22.5 T and 4.2 K, the highest value ever reported in any 122 phase.