A coarse-grained model is developed to allow large-scale molecular dynamics (MD) simulations of a branched polyetherimide derived from two backbone monomers [4,4'-bisphenol A dianhydride (BPADA) and m-phenylenediamine (MPD)], a chain terminator [phthalic anhydride (PA)], and a branching agent [tris[4-(4-aminophenoxy)phenyl] ethane (TAPE)]. An atomistic model is first built for the branched polyetherimide. A systematic protocol based on chemistry-informed grouping of atoms, derivation of bond and angle interactions by direct Boltzmann inversion, and parameterization of nonbonded interactions by potential of mean force (PMF) calculations via gas-phase MD simulations of atomic group pairs is used to construct the coarse-grained model. A six-pair geometry, with one atomic group at the center and six replicates of the other atomic group placed surrounding the central group in a NaCl structure, has been demonstrated to significantly speed up the PMF calculations and partially capture the many-body aspect of the PMFs. Furthermore, we propose a correction term to the PMFs that can make the resulting coarse-grained model transferable temperature-wise, by enabling the model to capture the thermal expansion property of the polymer. The coarse-grained model has been applied to explore the mechanical, structural, and rheological properties of the branched polyetherimide.