Broadly-neutralizing monoclonal antibodies are of high therapeutic utility against infectious diseases caused by bacteria and viruses, as well as different types of intoxications. Snakebite envenoming is one such debilitating pathology, which is currently treated with polyclonal antibodies derived from immunized animals. For the development of novel envenoming therapies based on monoclonal antibodies with improved therapeutic benefits, new discovery approaches for broadly-neutralizing antibodies are needed. Here, we present a methodology based on phage display technology and a cross-panning strategy that enables the selection of cross-reactive monoclonal antibodies that can broadly neutralize toxins from different snake species. This simple in vitro methodology is immediately useful for the development of broadly-neutralizing (polyvalent) recombinant antivenoms with broad species coverage, but may also find application in the development of broadly-neutralizing antibodies against bacterial, viral, and parasitic agents that are known for evading therapy via resistance mechanisms and antigen variation.