© 2019 National Academy of Sciences. All Rights Reserved. By investigating the bulk superconducting state via dc magnetization measurements, we have discovered a common resurgence of the superconducting transition temperatures (Tcs) of the mono-layer Bi2Sr2CuO6+δ (Bi2201) and bilayer Bi2Sr2CaCu2O8+δ (Bi2212) to beyond the maximum Tcs (Tc-maxs) predicted by the universal relation between Tc and doping (p) or pressure (P) at higher pressures. The Tc of underdoped Bi2201 initially increases from 9.6 K at ambient to a peak at 23 K at 26 GPa and then drops as expected from the universal Tc-P relation. However, at pressures above 40 GPa, Tc rises rapidly without any sign of saturation up to 30 K at 51 GPa. Similarly, the Tc for the slightly overdoped Bi2212 increases after passing a broad valley between 20 and 36 GPa and reaches 90 K without any sign of saturation at 56 GPa. We have, therefore, attributed this Tc resurgence to a possible pressure-induced electronic transition in the cuprate compounds due to a charge transfer between the Cu 3dx2−y2 and the O 2p bands projected from a hybrid bonding state, leading to an increase of the density of states at the Fermi level, in agreement with our density functional theory calculations. Similar Tc-P behavior has also been reported in the trilayer Br2Sr2Ca2Cu3O10+δ (Bi2223). These observations suggest that higher Tcs than those previously reported for the layered cuprate high-temperature superconductors can be achieved by breaking away from the universal Tc-P relation through the application of higher pressures.