Improving the precision of self-consistent-charges density-functional tight-binding method (SCC-DFTB) without losing its computational efficiency is primarily thought and hoped to be possible, if possible at all, by moving beyond its current two-centre-approximative tight-binding structure and the second-order nature of SCC. In this paper, however, we point out that there may still be possibilities of making it more precise without such an extension. Two improvements within the very second-order SCC are proposed here. First, inclusion of a multipole expansion of interacting atomic charge fluctuations, and second, a semi-empirical refinement of their interaction potential profiles and their self-interaction energies. Besides showing in detail what is to be improved with respect to the current SCC-DFTB realizations, we fully derive the respective new formulas ready to implement.