We numerically and experimentally report flexible spectrum sharing of two asynchronous phase-shift keying (PSK) signals using power division multiplexing. We show that a hybrid quadrature-amplitude-modulated signal is generated when two PSK signals with different power levels are superposed. By using successive interference cancellation, a 20 Gbaud "strong" signal combined with a 9 or 4 Gbaud "weak" signal can be recovered sequentially with bit-error rate performance below the forward error correction threshold. In addition, we show the dependence of system performance on the power ratio between the strong and weak signals. These two signals can contain different baudrates, pulse shapes, and modulation formats.