We report on the development of many-body density functional tight binding (DFTB) models for carbon, which include either explicit or implicit calculation of multi-center terms in the Hamiltonian. We show that all of our methods yield accurate eigenstates and eigenfunctions for both ambient diamond and transitions to molten, metallic states. We then determine a three-body repulsive energy to compute accurate equation of state and structural properties for carbon under these conditions. Our results indicate a straightforward approach by which many-body effects can be included in DFTB, thus extending the method to a wide variety of systems and thermodynamic conditions. (c) 2014 Published by Elsevier B.V.