Bare and gold-coated tilted fiber Bragg gratings (TFBGs) can nowadays be considered as a mature technology for volume and surface refractometric sensing, respectively. As for other technologies, a continuous effort is made towards the production of even more sensitive sensors, thereby enabling a high-resolution screening of the surroundings and the possible detection of rare events. To this aim, we study in this work the development of TFBG refractometers in 4-core fibers. In particular, we show that the refractometric sensitivity of the cut-off mode can reach 100 nm/RIU for a bare grating. Using another demodulation method, a tenfold sensitivity increase is obtained when tracking the extremum of the SPR (surface plasmon resonance) envelope for a gold-coated TFBG configuration. Immobilization of DNA probes was performed as a proof-of-concept to assess the high surface sensitivity of the device.