Adequately designed multiresponsive water-soluble graft copolymers were used to serve as a multifunctional polymeric platform for the encapsulation and transfer in aqueous media of hydrophobic magnetic nanoparticles (MNPs). The backbone of the graft copolymers was composed of hydrophilic sodium methacrylate units, hydrophobic dodecyl methacrylate units, and luminescent quinoline-based units, while either the homopolymer poly(N-isopropylacrylamide) or a poly(N,N-dimethylacrylamide-co-N-isopropylacrylamide) copolymer was used as thermosensitive pendent side chains. The polymeric platform forms micellar-type assemblies in aqueous solution, and exhibits pH-responsive luminescent properties and a lower critical solution temperature behavior in water. Depending on the design of the side chains, the cloud point temperatures were determined at 38 and 42 °C, close or slightly above body temperature (37 °C). Above the critical micelle concentration (CMC), both graft copolymers can effectively stabilize in aqueous media as magnetic colloidal superparticles (MSPs), oleylamine-coated MnFe2O4 MNPs, as well as 1:1 mixture of oleylamine-coated MnFe2O4 and CoFe2O4 MNPs. When CoFe2O4 particles were mixed with MnFeO4 in equal amounts, the specific loss power increased significantly, while an opposite trend was observed in the magnetic resonance imaging (MRI) studies, probably due to the anisotropy of cobalt. As a consequence, fine-tuning of the chemical structure of the copolymers and the composition of the MSPs can lead to materials that are able to act simultaneously as luminescent, hyperthermia, and contrast MRI agents.