The application of GPS in bridge monitoring aims to determine accurately and precisely the response of the deck and towers of the bridge and estimate the main response characteristics (amplitude and modal frequencies). The main requirement of GPS monitoring is a high level of accuracy and availability of fixed solutions, which ensure the reliable operation of GPS and result in the precise estimation of the bridge's response. However, the derived GPS time series of bridge monitoring can be contaminated by noise, due to the performance of the GPS satellite(s), the geometry of the GPS satellite constellation and the potential obstructions due to the bridge elements, which can even lead to GPS solution of poor accuracy and/or precision and result in reduced efficiency of the performance of the GPS monitoring. This study investigates the potential contribution of other Global Navigation Satellite Systems (GNSS) constellations for a more robust and reliable displacement time series solution, derived from multi-GNSS records. More specifically, a novel method is developed to derive the optimal combination of GNSS records to determine the GNSS displacement time series based on checks of parameters which reflect the geometry of the satellite constellation and the quality of the GNSS satellites signals. The method is applied in monitoring of the Severn Suspension Bridge, in the United Kingdom, and it is revealed the enhancement in the GNSS monitoring performance of the bridge response for specific time intervals for various locations on the bridge's support towers, suspension cables and deck.