The Belinfante spin momentum (BSM) is a fundamental yet enigmatic quantity of electromagnetic fields. It vanishes from the global momentum of the field, but can be detected locally, manifesting itself as an optical force on small particles. Hitherto, however, the BSM force is a concept well established only within the dipole approximation, and there is no explicit experimental evidence for its action on multipoles. Here, a theoretical model for multipolar BSM forces, exerted on generic Mie particles supporting multipoles of arbitrary order, is developed. This multipolar mechanical action is observed experimentally from a structured light field, which suppresses the effect of spin-orbit coupling. It can also selectively enhance the multipolar BSM forces, while restraining the dipolar component on a probe particle (Au sphere). These results constitute a distinct chapter in the physics of high-order interactions in light-matter systems and can facilitate additional progress in optomechanics, optical manipulation, and Mie-tronics.