The 2D material tin selenide monolayer (SnSe) has attracted a lot of attention due to its excellent optoelectronic properties. This study focuses on the investigation of the potential improvement of the response of surface plasmon resonance (SPR) sensors by coating the gold layer with SnSe allotrope (α, δ, ε) monolayers. Using an optimization algorithm along with the transfer matrix method (TMM), we determined the optimal thickness of the gold layer as a function of the number of monolayers added to significantly increase the sensor’s response in terms of reflectivity and phase. With respect to reflectivity, sensitivity increased by 20% in comparison with the optimal bare gold structure, whilst with respect to phase, sensitivity was approximately two orders of magnitude greater than the bare gold structure. Our results demonstrate that SPR sensors modified with SnSe monolayers could be used in diagnostic applications where both high sensitivity and small concentration of analyte are required.