Experimental studies have shown that some proteins exist in two alternative native-state conformations. It has been proposed that such bi-stable proteins can potentially function as evolutionary bridges at the interface between two neutral networks of protein sequences that fold uniquely into the two different native conformations. Under adaptive conflict scenarios, bi-stable proteins may be of particular advantage if they simultaneously provide two beneficial biological functions. However, computational models that simulate protein structure evolution do not yet recognize the importance of bi-stability. Here we use a biophysical model to analyze sequence space to identify bi-stable or multi-stable proteins with two or more equally stable native-state structures. The inclusion of such proteins enhances phenotype connectivity between neutral networks in sequence space. Consideration of the sequence space neighborhood of bridge proteins revealed that bi-stability decreases gradually with each mutation that takes the sequence further away from an exactly bi-stable protein. With relaxed selection pressures, we found that bi-stable proteins in our model are highly successful under simulated adaptive conflict. Inspired by these model predictions, we developed a method to identify real proteins in the PDB with bridge-like properties, and have verified a clear bi-stability gradient for a series of mutants studied by Alexander et al. (Proc Nat Acad Sci USA 2009, 106:21149-21154) that connect two sequences that fold uniquely into two different native structures via a bridge-like intermediate mutant sequence. Based on these findings, new testable predictions for future studies on protein bi-stability and evolution are discussed.