We explore the impact of retaining three-body operators within the in-medium similarity renormalization group (IMSRG), as well as various approximations schemes. After studying two toy problems, idential fermions with a contact interaction and the Lipkin-Meshkov-Glick model, we employ the valence-space formulation of the IMSRG to investigate the even-A carbon isotopes with a chiral two-body potential. We find that retaining only those commutators expressions that scale as N7 provides an excellent approximation of the full three-body treatment.