The monopole monotron instability is a well-known phenomenon in the linear beam devices. In recent development of a high efficiency 50 MW X-band klystron such instabilities were found and mitigated in a special 2 nd harmonic multi-cell cavities triplet that is used to improve the klystron performance. In further simulations of the klystron, using 3D Particle-In-cell computer code, the more rare and complicated phenomenon, previously unreported in non-relativistic devices, associated with rotating multipolar monotron instabilities was discovered. In this letter, the qualitative and quantitative analysis of these oscillations will be presented. Various resonant multipolar instabilities suppression strategies will be introduced and discussed in detail.