Optoelectronic excitations in monolayer MoS2 manifest from a hierarchy of electrically tunable, Coulombic free-carrier and excitonic many-body phenomena. Investigating the fundamental interactions underpinning these phenomena - critical to both many-body physics exploration and device applications - presents challenges, however, due to a complex balance of competing optoelectronic effects and interdependent properties. Here, optical detection of bound- and free-carrier photoexcitations is used to directly quantify carrier-induced changes of the quasiparticle band gap and exciton binding energies. The results explicitly disentangle the competing effects and highlight longstanding theoretical predictions of large carrier-induced band gap and exciton renormalization in 2D semiconductors.