Assembling superparamagnetic particles into ordered lattices is an attractive means of generating new magnetically responsive materials, and is commonly achieved by tailoring interparticle interactions as a function of the ligand coating. However, the inherent linkage between the collective magnetic behavior of particle arrays and the assembly processes used to generate them complicates efforts to understand and control material synthesis. Here, we use a synergistic combination of a chemical force (hydrogen bonding) and magnetic dipole coupling to assemble polymer-brush coated superparamagnetic iron oxide nanoparticles, where the relative strengths of these interactions can be tuned to reinforce one another and stabilize the resulting superlattice phases. We find that we can precisely control both the dipole-dipole coupling between nanoparticles and the strength of the ligand-ligand interactions by modifying the interparticle spacing through changes to the polymer spacer between the hydrogen bonding groups and the nanoparticles' surface. This results in modulation of the materials' blocking temperature, as well as the stabilization of a unique superlattice phase that only exists when magnetic coupling between particles is present. Using magnetic interactions to affect nanoparticle assembly in conjunction with ligand-mediated interparticle interactions expands the potential for synthesizing predictable and controllable nanoparticle-based magnetic composites.