We have established a model for a weakly-coupled semiconductor superlattice (SL) with a shunting side layer and developed the numerical procedure to solve it. The shunt is used to stabilize the field configuration in the SL. The effects of the lateral size of the SL, the connectivity between the SL and shunt and other properties of the shunt are studied. Beyond a certain lateral size of the SL, the SL loses its lateral stability in spite of a good shunt. For a narrow SL, a high quality shunt can stabilize the whole SL while a bad quality shunt causes oscillations and field domains. Different bifurcation scenarios are observed varying the parameters.