QuCoM will explore the intricate interplay between quantum mechanics and gravity within a parameter range accessible for cost-effective table-top experiments. The project will achieve this by suspending sub millimetre-sized particles in carefully designed optical and magnetic traps. These suspended particles will then be used to detect gravitational forces in an unprecedented mass regime, opening new avenues in experimental physics. Additionally, QuCoM will investigate the fascinating realm of quantum superpositions, addressing scenarios where such masses are quantum mechanically delocalized in space. Supported by a substantial grant of 2.3 million Euros, the project is poised to address some of the most prominent theoretical proposals that combine quantum physics and gravity in nonstandard ways. By rigorously assessing the limits of validity of these proposals and further constraining the values of their parameters, QuCoM aims to make significant contributions to our understanding of the fundamental principles governing the universe.