Exceptional points (EPs) are degeneracies occuring in open systems described by complex eigenvalues. Near an EP, the system eigenvalues exhibit a topological structure that leads to interesting behavior with respect to closed adiabatic cycles. Here, I will present our work on exploring EP phenomena in an optomechanical system. Using nearly-degenerate mechanical modes of a Si3N4 membrane, we demonstrate energy transfer via encircling of an EP, as well as non-reciprocal behavior arising from a breakdown of adiabaticity. I'll also discuss recent work on achieving the same physics with non-degenerate modes, using a bichromatic drive scheme.