Current experimental realizations of the quantum anomalous Hall phase in both electronic and photonic systems have been limited to a Chern number of one. In photonics, this corresponds to a single-mode one-way edge waveguide. Here, we predict quantum anomalous Hall phases in photonic crystals with large Chern numbers of 2, 3, and 4. These new topological phases were found by simultaneously gapping multiple Dirac and quadratic points. We demonstrate a continuously tunable power splitter as a possible application of multimode one-way waveguides. All our findings are readily realizable at microwave frequencies.