We present the excitonic configuration interaction (ECI) method-a fragment-based analogue of the CI method for electronic-structure calculations of the multichromophoric systems. It can also be viewed as a generalization of the exciton approach which (i) allows embedding via point charges with arbitrary values in the site-state calculation, (ii) includes multi-local excitation (MLE) products of site states in the excitonic basis, in addition to the ground-state (GS) and local excitation (LE) products, and (iii) takes into account all contributions to the full-system Hamiltonian matrix elements within the strongorthogonality assumption. Regarding (i), we present the excitonic analogue of the Hartree-Fock method-called the EHF approach-which finds the embedding charges that minimize the energy of the GS product. In (ii), one can restrict the excitation rank of the employed excitonic basis, which results in truncated-CI-like expansions (ECIS includes GS and LE products, ECISD additionally includes two-fragment excitation, etc.). The expressions for the matrix elements in (iii) are obtained within McWeeny's group function theory, generalized to accommodate the flexible embedding in (i).