The application of pressure can induce transitions between unconventional quantum phases in correlated materials. The inorganic compound TiOCl, composed of chains of S=1/2 Ti ions, is an ideal realization of a spin-Peierls system with a relatively simple unit cell. At ambient pressure, it is an insulator due to strong electronic interactions (a Mott insulator). Its resistivity shows a sudden decrease with increasing pressure, indicating a transition to a more metallic state which may coincide with the emergence of charge density wave order. Therefore, high pressure studies of the structure with x-rays are crucial in determining the ground-state physics in this quantum magnet. In ambient pressure, TiOCl exhibits a transition to an incommensurate nearly dimerized state at $T_{c2}=92$ K and to a commensurate dimerized state at $T_{c1}=66$ K. Here, we discover a rich phase diagram as a function of temperature and pressure using x-ray diffraction on a single crystal in a diamond anvil cell down to $T=4$ K and pressures up to 14.5 GPa. Remarkably, the magnetic interaction scale increases dramatically with increasing pressure, as indicated by the high onset temperature of the spin-Peierls phase. At $sim$7 GPa, the extrapolated onset of the spin-Peierls phase occurs above $T=300$ K, indicating a quantum singlet state exists at room temperature. Further comparisons are made with the phase diagrams of related spin-Peierls systems that display metallicity and superconductivity under pressure.