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One of the primary goals for the researchers is to create a high-quality sensor with a simple structure because of the urgent requirement to identify biomolecules at low concentrations to diagnose diseases and detect hazardous chemicals for health early on. Recently graphene has attracted much interest in the field of improved biosensors. Meanwhile, graphene with new materials such as CaF2 has been widely used to improve the applications of graphene-based sensors. Using the fantastic features of the graphene/CaF2 multilayer, this article proposes an improvement sensor in the sensitivity (S), the figure of merit (FOM), and the quality factor (Q). The proposed sensor is based on the five-layers graphene/dielectric grating integrated with a Fabry–Perot cavity. By tuning graphene chemical potential (µc), due to the semi-metal features of graphene, the surface plasmon resonance (SPR) waves excited at the graphene/dielectric boundaries. Due to the vertical polarization of the source to the gratings and the symmetry of the electric field, both corners of the grating act as electric dipoles, and this causes the propagation of plasmonic waves on the graphene surface to propagate towards each other. Finally, it causes Fabry–Perot (FP) interference on the surface of graphene in the proposed structure's active medium (the area where the sample is located). In this article, using the inherent nature of FP interference and its S to the environment's refractive index (RI), by changing a minimal amount in the RI of the sample, the resonance wavelength (interferometer order) shifts sharply. The proposed design can detect and sense some cancers, such as Adrenal Gland Cancer, Blood Cancer, Breast Cancer I, Breast Cancer II, Cervical Cancer, and skin cancer precisely. By optimizing the structure, we can achieve an S as high as 9000 nm/RIU and a FOM of about 52.14 for the first resonance order (M1). Likewise, the remarkable S of 38,000 nm/RIU and the FOM of 81 have been obtained for the second mode (M2). In addition, the proposed label-free SPR sensor can detect changes in the concentration of various materials, including gases and biomolecules, hemoglobin, breast cancer, diabetes, leukemia, and most alloys, with an accuracy of 0.001. The proposed sensor can sense urine concentration with a maximum S of 8500 nm/RIU and cancers with high S in the 6000 nm/RIU range to 7000 nm/RIU. Also, four viruses, such as M13 bacteriophage, HIV type one, Herpes simplex type 1, and influenza, have been investigated, showing Maximum S (for second resonance mode of λR(M2) of 8000 nm/RIU (λR(M2) = 11.2 µm), 12,000 nm/RIU (λR(M2) = 10.73 µm), 38,000 nm/RIU (λR(M2) = 11.78 µm), and 12,000 nm/RIU (λR(M2) = 10.6 µm), respectively, and the obtained S for first resonance mode (λR(M1)) for mentioned viruses are 4740 nm/RIU (λR(M1) = 8.7 µm), 8010 nm/RIU (λR(M1) = 8.44 µm), 8100 nm/RIU (λR(M1) = 10.15 µm), and 9000 (λR(M1) = 8.36 µm), respectively. [ABSTRACT FROM AUTHOR]