Polystyrene-interleaved carbon fibre reinforced epoxy composites exhibiting controllable stiffness have been manufactured. These composites undergo reductions in flexural stiffness of up to 99% when heated above the glass transition temperature Tg of the interleaf layers. Potential applications for such materials include their use in morphing and deployable structures. Flexural tests at room temperature indicated that improvements in adhesion between the polystyrene and CFRP layers are required to prevent premature failure of the composites at low shear stresses. Here we investigate how modification of the interleaf layer improves the interlaminar shear strength of the laminates without affecting the stiffness loss at elevated temperatures. Two poly(styrene-co-maleic anhydride) (SMA) films with different maleic anhydride content were prepared and used as interleaf films. Thick adherend shear tests showed that the adhesion strength more than doubled, while flexural tests showed that composites containing SMA interleafs had more than twice the apparent flexural strength of composites containing pure polystyrene layers at 25 °C and yet still undergo significant reductions in stiffness at elevated temperature.