The necessity to improve magnetic building blocks in magnetic nano-structured soft materials stems from a fascinating potential these materials have in bio-medical applications and nanofluidics. Along with practical reasons, the interplay of magnetic and steric interactions on one hand, and entropy, on the other, makes magnetic soft matter fundamentally challenging. Recently, in order to tailor magnetic response of the magnetic particle suspensions, the idea arose to replace standard single-core nanoparticles with nano-sized clusters of single-domain nanoparticles (grains) rigidly bound together by solid polymer matrix - multicore magnetic nanoparticles (MMNPs). To pursue this idea, a profound understanding of the MMNP interactions and self-assembly is required. In this work we present a computational study of the MMNP suspensions and elucidate their self-assembly and magnetic susceptibility. We show that depending on the magnetic moment of individual grains the suspensions exhibit qualitatively distinct regimes. Firstly, if the grains are moderately interacting, they contribute to a significant decrease of the remanent magnetisation of MMNPs and as such to a decrease of the magnetic susceptibility, this way confirming previous findings. If the grains are strongly interacting, instead, they serve as anchor points and support formation of grain clusters that span through several MMNPs, leading to MMNP cluster formation and a drastic increase of the initial magnetic response. Both the topology of the clusters and their size distribution in MMNP suspensions is found to be notably different from those formed in conventional magnetic fluids or magnetorheological suspensions.