Previous work by D. C. Ronquillo and M. R. Peterson has strongly suggested the existence of a topologically ordered quantum spin liquid phase in the intermediate regime of the antiferromagnetic Heisenberg model on the Shastry-Sutherland lattice. There are a number of physical systems, such as SrCu₂(BO₃)₂), ErB₄, and TmB₄, that are well approximated by the aforementioned model. However, realistic effects such as next-nearest neighbor spin-spin interactions could have non-trivial effects on the phase diagram or even on the existence of the topologically ordered spin liquid. In this work we modify the Shastry-Sutherland lattice by introducing the next-nearest diagonal bonds J₃ to study how the system changes in response to strength variations of these extra bonds, as well as the variations in the traditional J₂ bonds. We calculate the lowest-lying energies via exact diagonalization on a cluster of 24 spins, and summarize our results with a phase diagram showing regions of Neel, quantum spin liquid, and VBC phases. We then characterize the ground states by computing the topological entanglement entropy as a function of J2 and J3 using the Kitaev-Preskill construction method and discuss the order of the transitions between the different phases observed.