Tunable magnon propagation is essential for constructing magnonic devices. The magnonic spin-valve effect was recently realized in a magnetic bilayer heterostructure. Similar to a standard electronic spin valve, switching from parallel to antiparallel magnetic orientations in the bilayer achieves comparatively high and low polarized magnon transmission. Here, we propose a trilayer magnonic spin-valve structure to improve controllability over polarized magnon propagation. In addition to high and low magnon transmission, we find a medium magnon transmission behavior, where magnons from the bottom layer jump across the middle magnetic layer and land in the top layer. Coupled magnon modes in the trilayer structure give rise to the magnon transmission feature. We investigate the effects of the external magnetic field and spin-orbit torque, and we can drive a $150%$ change in the medium transmission without magnetization reversal. This effect avoids the slow reversal process and increases the trilayer valve's flexibility. These findings render the possibility of dynamically manipulable magnonic information devices with multiple output states.