A generalization of the concept of multimode interference sensors is presented here for the first time, to the best of our knowledge. The existing bimodal and trimodal sensors correspond to particular cases of those interference sensors. A thorough study of the properties of the multimode waveguide section provided a deeper insight into the behavior of this class of sensors, which allowed us to establish new criteria for designing more sensitive structures. Other challenges of using high-order modes within the sensing area of the device reside in the excitation of these modes and the interpretation of the output signal. To overcome these, we developed a novel structure to excite any desired high-order mode along with the fundamental mode within the sensing section, while maintaining a fine control over the power distribution between them. A new strategy to detect and interpret the output signal is also presented in detail. Finally, we designed a high-order sensor for which numerical simulations showed a theoretical limit of detection of 1.9 × 10−7 RIU, making this device the most sensitive multimode interference sensor reported so far.