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We report the results of a globally coordinated photometric campaign to search for transits by the P ~ 30 day and P ~ 60 day outer planets of the three-planet system orbiting the nearby M dwarf Gl 876. These two planets experience strong mutual perturbations, which necessitate the use of a dynamical (four-body) model to compute transit ephemerides for the system. Our photometric data have been collected from published archival sources, as well as from our photometric campaigns that were targeted to specific transit predictions. Our analysis indicates that transits by planet c (P ~ 30 days) do not currently occur, in concordance with the best-fit i = 50° coplanar configuration obtained by dynamical fits to the most recent radial velocity data for the system. Transits by planet b (P ~ 60 day) are not entirely ruled out by our observations, but our data indicate that it is very unlikely that they occur. Our experience with the Gl 876 system suggests that a distributed ground-based network of small telescopes can be used to search for transits of very low mass M stars by terrestrial-sized planets.