Magnetoplasmonics is highly promising to devise active optical elements: modulating the plasmon resonance condition with magnetic field can boost the performance of refractometric sensors and nanophotonic optical devices. Nevertheless, real life applications are hampered by the magnetoplasmonic trilemma: 1) a good plasmonic metal has sharp optical resonances but low magneto-optical response; 2) a magnetic metal has strong magneto-optical response but a very broad plasmonic resonance; 3) mixing the two components degrades the quality of both features. To overcome the trilemma, we use a different class of materials, transparent conductive oxide nanocrystals (NCs) with plasmonic response in the near infrared. Although non-magnetic, they combine a large cyclotron frequency (due to small electron effective mass) with sharp plasmonic resonances. We benchmark the concept with F- and In- doped CdO (FICO) and Sn-doped In2O3 (ITO) NCs to boost the magneto-optical Faraday rotation and ellipticity, reaching the highest magneto-optical response for a non-magnetic plasmonic material, and exceeding the performance of state-of-the-art ferromagnetic nanostructures. The magnetoplasmonic response of these NCs was rationalized with analytical model based on the excitation of circular magnetoplasmonic modes. Finally, proof of concept experiments demonstrated the superior performance of FICO NCs with respect to current state of the art in magnetoplasmonic refractometric sensing, approaching the sensitivity of leading localized plasmon refractometric methods with the advantage of not requiring complex curve fitting.