Large-scale superconductor applications necessitate a superconducting matrix with pinning sites (PSs) that immobilize vortices at elevated temperatures and magnetic fields. While previous works focused on the single addition of nanoparticles, the simultaneous inclusion of different nanoparticles into a superconducting matrix can be an effective way to achieve an improved flux pinning capacity. The purpose of this study is to explore the influence of mixed-nanoparticle pinning, with the co-addition of non-magnetic (BaTiO3; BT) and various types of magnetic spinel ferrite (MFe2O4, abbreviated as MFO, where M = Mn, Co, Cu, Zn, and Ni) nanoparticles, on the superconductivity and flux pinning performances of the high-temperature superconductor YBa2Cu3Oy (YBCO). An analysis of X-Ray diffraction (XRD) data of BT–MFe2O4-co-added YBCO samples showed the formation of an orthorhombic structure with Pmmm symmetry. According to electrical resistivity measurements, the emergence of the superconducting state below Tcoffset (zero-resistivity temperature) was proven for all samples. The highest Tcoffset value was recorded for the Y-BT-MnFO sample, while the minimum value was obtained for the Y-BT-ZnFO sample. Direct current (DC) magnetization results showed good magnetic flux pinning performance for all the co-added samples compared to the pristine sample but with some discrepancies. At 77 K, the values of the self-critical current density (self-Jcm) and maximum pinning force (Fpmax) for the Y-BT-MnFO sample were found to be eight times higher and seventeen times greater than those for the pristine sample, respectively. The results acquired suggested that mixing the BT phase with an appropriate type of spinel ferrite nanoparticles can be a practical solution to the problem of degradation of the critical current density of the YBCO material.