Raspberry-like metamolecules (RMMs), clusters of closely packed noble metal nanobeads self-assembled on a dielectric core, exhibit emergent optical properties not available in simple nanoparticles. Examples include broad band far-field extinction and artificial optical magnetism. An important feature of these clusters is that their magnetic plasmon resonance and the breadth of their extinction spectra can be tuned via simple synthetic routes, such as by changing the bead size, core size, or the average interbead distance. However, the effect of each of these variables on the final magnetic resonance frequency and strength has not been studied in depth. Understanding how to tune the electric and magnetic resonance modes in these clusters can help improve the design of novel metamaterials for various applications. In this article, we combine theoretical analyses using numerical finite-different time-domain modeling and analytical dipole-dipole coupling theory to study the role of these variables in the global electric and global magnetic dipole modes of RMMs. We also demonstrate that these variables can be readily controlled experimentally using surfactants with varying lengths or changing synthetic conditions and show that the experimental results are consistent with theoretical predictions. The results provide a guideline for synthesizing plasmonic nanoparticle assemblies when specific resonant frequencies and bandwidths are desired.