Multicomponent nanoparticle superlattices (SLs) promise the integration of nanoparticles (NPs) with remarkable electronic, magnetic, and optical properties into a single structure. Here, we demonstrate that heterodimers consisting of two conjoined NPs can self-assemble into novel multicomponent SLs with a high degree of alignment between the atomic lattices of individual NPs, which has been theorized to lead to a wide variety of remarkable properties. Specifically, by using simulations and experiments, we show that heterodimers composed of larger Fe3O4 domains decorated with a Pt domain at one vertex can self-assemble into an SL with long-range atomic alignment between the Fe3O4 domains of different NPs across the SL. The SLs show an unanticipated decreased coercivity relative to nonassembled NPs. In situ scattering of the self-assembly reveals a two-stage mechanism of self-assembly: translational ordering between NPs develops before atomic alignment. Our experiments and simulation indicate that atomic alignment requires selective epitaxial growth of the smaller domain during heterodimer synthesis and specific size ratios of the heterodimer domains as opposed to specific chemical composition. This composition independence makes the self-assembly principles elucidated here applicable to the future preparation of multicomponent materials with fine structural control.