In this paper, we analyzed the sensing performance of the multifunctional surface plasmon resonance (SPR) biosensors based on bimetallic film (Ag/Al2O3), and a hybrid nanostructure of BaTiO3 and 2D nanomaterials (Ti3C2T, black phosphorus and BlueP/MoS2 heterostructure). Using excitation light at 633 nm, we numerically analyze performance such as angular sensitivity, peak sensitivity, figure of merit, and electric field strength. The study shows the proposed biosensor design exhibits a highest sensitivity of 504 deg/RIU with a 320% improvement over the conventional SPR sensor reported so far on similar 2D nanomaterials, and can also maintain a good quality SPR curve. The results of different proposed and optimized nano-configurations show that the improved angular sensitivity of 120%, 60%, 290% and 80% for BaTiO3, Ti3C2T, Black phosphorus and BlueP/MoS2, respectively, for a change in the refractive index (RI) of the sensing medium of RIU. Similarly, the variation in field intensity at the sensing interface further confirms the high sensitivity obtained for our proposed SPR biosensor. Therefore, our proposed design would be practically suitable for biosensing with higher performance with the available fabrication technologies.