Low acoustic loss suspension systems are essential components in low thermal noise instruments including gravitational wave detectors. Monolithic fused silica suspensions have been used successfully with fused silica test masses but may not be suitable in next generation detectors that may use sapphire or silicon test masses. Here we report a study of a modular suspension system with high replaceability. The system is based on high pressure gravitationally attached mechanical contacts which have been previously shown to contribute low acoustic losses to sapphire resonators. Here we combine high pressure contacts with cantilevers and fibres to create sets of four suspension modules which are shown to have low loss contributions to fused silica test masses in a 74-m high-finesse optical cavity. Results are combined with finite element simulations to estimate the strain energy distributions of the eigenmodes. By combining the simulations and measurement results, the test mass loss angle due to the coupling to the suspension system was estimated. The modular suspension system is shown to contribute <10% to the total test mass acoustic loss. Such suspension systems could have applications for test masses or subsystems in next generation gravitational wave detectors.