We report on quantum-interference measurements in top-gated Hall bars of monolayer graphene epitaxially grown on the Si face of SiC, in which the transition from negative to positive magnetoresistance was achieved varying temperature and charge density. We perform a systematic study of the quantum corrections to the magnetoresistance due to quantum interference of quasiparticles and electron-electron interaction. We analyze the contribution of the different scattering mechanisms affecting the magnetotransport in the $-2.0 times 10^{10}$ cm$^{-2}$ to $3.75 times 10^{11}$ cm$^{-2}$ density region and find a significant influence of the charge density on the intravalley scattering time. Furthermore, we observe a modulation of the electron-electron interaction with charge density not accounted for by present theory. Our results clarify the role of quantum transport in SiC-based devices, which will be relevant in the development of a graphene-based technology for coherent electronics.