Nonreciprocal electromagnetic wave transmission, essential for wireless communication, quantum computing, and radar systems, traditionally relies on breaking time-reversal symmetry through static magnetic fields or structural modifications, which face limitations in tunability and integration. Recent advancements in cavity magnonics, particularly the use of bound states in the continuum (BIC) and pump-induced magnon mode (PIM), have enabled enhanced nonreciprocal isolation and dynamic control of magnon dynamics. This study show a novel method to achieve broadband-tunable microwave nonreciprocal isolation by introducing multiple modulated pump signals, thereby extending conventional single-mode magnon-based nonreciprocal transmission to multi-channel and broadband regimes. The core approach involves exciting multiple PIMs in a cavity magnonics system and enabling their strong coupling with BIC, generating hybrid modes with pronounced nonreciprocal characteristics. The experimental setup comprises a 1-millimeter-diameter yttrium iron garnet (YIG) sphere positioned at the node of a microwave resonator (central frequency: 2.92 GHz), with pump signals injected through a microwave patch antenna. By dynamically tuning the frequency, power, and number of pump signals, we demonstrate precise control over the number of nonreciprocal isolation channels and their spectral positions. Notably, continuous tuning of the nonreciprocal bandwidth was achieved by increasing the number of pump signals from 2 to 5, expanding the isolation bandwidth from 6 MHz to 14 MHz. Furthermore, by tailoring the spectral distribution of pump signals, the system realizes flexible switching between bandpass and band-stop isolation states. Importantly, this method eliminates the need for static magnetic field adjustments or structural reconfiguration, relying solely on coherent microwave-photon interactions to modulate PIM-BIC coupling. Experimental results highlight two key physical outcomes: (1) Extension of conventional single-mode magnonic nonreciprocal transmission to multi-channel and broadband-tunable regimes; (2) Achieving microwave nonreciprocal control without the need for static magnetic field adjustments or structural reconfiguration. These advances establish a robust platform for designing reconfigurable multi-channel isolators and circulators, with direct applications in microwave communication systems, quantum information processing, and radar technologies.