Multistable switches are hallmarks of decision-making processes that play crucial roles in dictating cell fate transitions during lineage specification, cell division cycle and cell death. A multistable switch possesses multiple stable attractors or stable steady states separated by unstable steady states. In order to investigate multistability in feedback regulated reaction networks, we developed a method of bifurcation analysis based on pseudo-potential energy of nonlinear dynamical systems. By defining an effective pseudo-potential energy of the chemical system in reduced dimension and monitoring the creation/annihilation of the extrema in the potential landscape, we performed multi-parameter bifurcation analyses in a high throughput automated fashion. We used this method to determine the design principles of regulatory motifs in generating tristable and a large variety of noncanonical bistable switches. The largescale bifurcation analysis also allowed us to determine robustness of network motifs in generating reliable response under extrinsic noise.