It is shown that nonlinear left-hand polarized waves can either stabilize or destabilize linear right-hand polarized instabilities triggered by an alpha particle beam in a magnetized electron proton plasma. For differential alpha particle speeds above the threshold for instability the destabilization depends upon the plasma ¿i = vth.i/vA, where vth.i is the thermal velocity of the i plasma component and vA is the Alfv¿n velocity. For any given finite-amplitude wave frequency, there is always a ¿i value such that above this value the system is destabilized further. For drift alpha particle speeds well above the instability threshold the destabilization can occur for any ¿i. It is also shown that the presence of the large-amplitude wave can trigger purely electrostatic ion-acoustic instabilities. The unstable waves are supported by the proton core.