A series of novel salts based on aromatic polyamines and 2,3-pyrazinedicarboxylic acid, such as C10H12N6O5 (1), C10H9ClN6O4 (2), C11H10N8O4 (3), and C14H17N16O5.5 (4) or 3,4-thiophenedicarboxylic acid, such as C10H10N4O4S (5), C10H9ClN4O4S (6), and C10H10N4O4S2 (7), were synthesized and characterized by single-crystal X-ray diffraction. All compounds crystallize in a monoclinic space group. The structure was subjected to complex Hirshfeld surface analysis, molecular electrostatic potential, enrichment ratio, and energy framework calculations. The influence of different cations on the packing of 3-carboxypyrazine-2-carboxylate and 4-carboxythiophene-3-carboxylate anions in the crystal lattice was studied. O…H/H…O interactions are the main contributor in all crystals. In addition, in a series of pyrazine-containing structures, N(C)…H/H…N(C) interactions have relevance, while in a series of thiophene-based compounds, C…H/H…C and S…H(O)/H(O)…S. In addition, Cl-based interactions are observed in compound 2. According to the enrichment ratio calculations, O…H/H…O and C…C are the most preferable interactions in all structures. The energy frameworks are dominated by the dispersive contribution, only in compound 3 is the electrostatic term dominant. The analyzed structures reveal intra- and intermolecular recurrent supramolecular synthons. In both series of crystals, the robust H-bonded centrosymmetric dimer R22(8) as homo- or as heterosynthon (in compounds 2, 3, 6, and 7) and the intramolecular synthon S(7) generated by O-H…O interactions (in compounds 2, 6, and 7) are present. The supramolecular patterns formed by π…π (C…C) and C-O(Cl,S)…C are also noticeable. Notably, a dual synthon linking the supramolecular chain via π…π interactions and the homosynthon R22(8) via N-H…N interactions is visible in both series of new salts. A library of H-bonding motifs at diverse levels of supramolecular architecture is provided. We extended the analysis of intramolecular H-bonding motifs to similar structures deposited in the Cambridge Structural Database. Another important feature is the existence of an intramolecular O…H…O bridge between two neighboring carboxylic groups as substituents in anions in compounds 3 and 5. In this context, we performed quantum theory of atoms-in-molecule calculations to reveal more details.