This letter presents an effective digital passive intermodulation (PIM) cancellation technique for multi-band multiple-input multiple-output frequency-division duplexing radios for 5G and beyond. We begin by introducing a universal PIM signal model for multi-band radios with an arbitrary number of transmit--receive antennas, which enables the calculation of basis functions at all intermodulation frequencies. After establishing this signal model, a comparative analysis of state-of-the-art behavioral models is conducted in the context of PIM modeling.