Though the DFTB/ChIMES model developed here is trained on molecular (gas phase) data, we have also tested its performance in reproducing the structural properties of graphite and diamond. These systems were chosen due to the fact that they contain a single element only while still probing different types of chemical bonds. In conclusion, we have shown that ChIMES can be used to extend DFTB to hybrid functional accuracy or greater. ChIMES parameters are determined rapidly through linear optimization, creating a beyond-pairwise interaction potential for DFTB. DFTB/ChIMES has the capability of reproducing vast quantities of high-level reference data while requiring only a small fraction of it for training. The accuracy of DFTB/ChIMES is discussed for total energies, atomic forces, isomerization energies, and vibrational frequencies across the vast conformational diversity of organic molecules in several popular datasets, as well as for the dihedral rotation energy profile of n-butane. Preliminary testing on solid carbon allotropes at ambient conditions show that DFTB/ChIMES is able to reproduce the experimental structure of graphite (a well-known challenge for standard DFT) as well as bulk diamond properties, while having been determined from gas-phase cluster data, only. On the basis of the results presented here, DFTB/ChIMES represents a promising direction for developing general purpose quantum models that are applicable to a wide range of materials and conditions. The small training set required by our approach, as shown in this study, could yield significant advantages for future development of computational models with a coupled cluster accuracy, significantly improved scaling, and high efficiency. The utility and ease of parameterization of DFTB/ChIMES allows for high-level quantum theory accuracy in the systems where traditional methods are far too computationally intensive for use.