Ba(Fe(1-x)Co(x))(2)As(2) 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, J(c). Moreover, FBS are very sensitive to strain, which induces an important enhancement in critical temperature, T(c), of the material. In this paper we demonstrate that strain induced by the substrate can further improve J(c) of both single and multilayer films by more than that expected simply due to the increase in T(c). The multilayer deposition of Ba(Fe(1-x)Co(x))(2)As(2) on CaF2 increases the pinning force density (F(p) = J(c) × µ0H) by more than 60% compared to a single layer film, reaching a maximum of 84 GN/m(3) at 22.5 T and 4.2 K, the highest value ever reported in any 122 phase.