Abstract: Quantum simulators have led to significant insight into the non-equilibrium behavior of quantum many-body systems. Programmable Rydberg atom simulators, in particular, have uncovered the existence of persistent oscillations of local observables due to the emergence of quantum many-body scars. The conventional understanding of these scar states purports that they form a small subset of non-ergodic eigenstates embedded in a thermal spectrum. In this talk, we will show that the PXP model, which closely describes strongly interacting Rydberg atoms, can exhibit many more scarred states than had been previously identified. We will present evidence that the magnetization and temporal correlators of the system exhibit oscillations for almost any initial product state with a frequency close to that of the conventional set of scars. We will argue that these oscillations arise due to multiple sets of scars that satisfy an approximate su(2) algebra. We will further explore the impact that this structure has on the system's dynamics in the presence of disorder. Finally, we will discuss a strategy to detect the presence of these new scarred states using quantum typically.