Graphene, as a two-dimensional magneto-optical material, supports magnetoplasmon polaritons (MPP) when exposed to an applied magnetic field. Recently, MPP of a single-layer graphene has shown an excellent capability in the modulation of near-field radiative heat transfer (NFRHT). In this study, we present a comprehensive theoretical analysis of NFRHT between two multilayered graphene structures, with a particular focus on the multiple MPP effect. We reveal the physical mechanism and evolution law of the multiple MPP, and we demonstrate that the multiple MPP allow one to mediate, enhance, and tune the NFRHT by appropriately engineering the properties of graphene, the number of graphene sheets, the intensity of magnetic fields, as well as the geometric structure of systems. We show that the multiple MPP have a quite significant distinction relative to the single MPP or multiple surface plasmon polaritons (SPPs) in terms of modulating and manipulating NFRHT. We demonstrate that this remarkable behavior is attributed to the coupling between the significant contributions of surface states at multiple surfaces and Shubnikov–de Haas-like oscillations in the spectrum, indicating a transformation of intraband and interband transitions. Notably, we find that the evolution from single MPP to multiple MPP is absolutely different from that from single SPPs to multiple SPPs. Finally, a thermal magnetoresistance effect and a negative-positive transition of the relative thermal magnetoresistance ratio are predicted in the multilayered system under consideration. Our study paves the way for a flexible control of NFRHT and it offers the possibility for the thermal photon-based communication technology and a magnetically controllable thermal switch.