A composite laminate with unsymmetric layup may exhibit two distinct stable configurations at room temperature due to the residual thermal stresses imparted during curing. This bistability leads unsymmetric composite laminates to be good candidates for adaptive flexible structures in particular for the fields of aerospace and aircraft. To extend the application potential of bistable composite laminates, the multistable behaviour of continuous compound composite surfaces are investigated. Two connection approaches are presented in this research. By tailoring the asymmetric bistability of indi- vidual composite elements, continuous surfaces composed of series-connected bistable composite shells demonstrate a high degree of multistability. This model can be developed to design longer composite surfaces possessing more stable shapes. In addition, a high degree of multistability is achieved by connecting square composite elements in a tessellated feature. By reducing the interactions between adjacent elements, a tessellated surface composed of n bistable elements shows a theoretical maximum 2n stable shapes. Finally, potential applications of highly multistable composite surfaces are introduced. The proposed multistable designs improve the flexible functionality of the adaptive structures.