We propose to study the pressure-dependence of the crystal structure of the alkaline earth copper phyllo-decaoxotetrasilicate Ba0.5Sr0.5CuSi4O10 to compliment our earlier studies of the low temperature behaviour and the compositional variation across the solid solution. Our rigid unit characterisation technique has allowed us to predict the behaviour of the unit cell to high accuracy and we have derived the first detailed structural model for how gillespite-structured phases behave in the P4/ncc phase. We predict a pressure-induced phase transition between 1 - 2 GPa to a P4212 phase and propose to carry out the first crystallographic examination of this phase.