Concave nanoparticles (NPs) with complex angled and non-Platonic geometries have unique optical, magnetic, catalytic, and biological properties originating from the singularities of the electrical field in apexes and craters. Preparation of such particles with a uniform size/shape and core-shell morphology represents a significant challenge, largely because of the poor knowledge of their formation mechanism. Here, this challenge is addressed and a study of the mechanism of their formation is presented for a case of complex spiky morphologiesthat led us to the conclusion that NPs with concave geometries can be, in fact, supraparticles (SPs) produced via the self-assembly of smaller convex integrants. This mechanism is exemplified by the vivid case of spiky SPs formed via the attachment of small and faceted Au NPs on smooth Au-coated iron oxide (Fe3O4@Au) seeds. The theoretical calculations of energies of primary interactionselectrostatic repulsion and van-der Waals repulsion, elaborated for this complex caseconfirm experimental observation and the self-limiting mechanism of SP formation. Besides demonstrating the mechanistic aspects of synthesis of NPs with complex geometries, this work also uncovers a facile approach for preparation of concave magnetoplasmonic particles. When combined with a spiky geometry, such bi-functional magnetoplasmonic SPs can serve as a unique platform for optoelectronic devices and biomedical applications.