Multilayer flows are oftensusceptible to interfacial instabilities caused due to jump in viscosity/elasticity across thefluid–fluid interface. It is frequently required to manipulate and control these interfacial instabilities in various applications such as coating processes or polymer coextrusion. We demonstrate here the possibility of using a deformable solid coating to control such interfacial instabilities for various flow configurations and for different fluid rheological behaviors. In particular, we show complete suppression of interfacial flow instabilities by making the walls sufficiently deformable when the configuration was otherwise unstable for the case of flow past a rigid surface. While these interfacial instabilities could be suppressed in certain parameter regimes, it is also possible to enhance the flow instabilities by tuning the shear modulus of the deformable solid coating for other ranges of parameters.