Five new multicomponent solid forms of the biologically active 1,2,4-thiadiazole derivative (TDZH) with dicarboxylic and hydroxybenzoic acids have been discovered by combined virtual/experimental cocrystal screening. The interplay between the intrinsic hierarchy of the donor/acceptor groups in the TDZH/coformer molecules and the hydrogen bond pattern in the multicomponent crystals was rationalized using quantitative analysis of molecular electrostatic potential (MEP) surfaces along with periodic DFT computations. All the TDZH cocrystals are based on a carboxy-aminothiadiazole heterosynthon which is stabilized by a combination of enthalpic factors and the “supramolecular chelating effect”. According to the analysis of the non-covalent interaction energies, the mean energy value of this heterosynthon equals ∼77 kJ mol⁻¹, which is comparable to the well-known carboxyl-amide and carboxyl-pyridine synthons in terms of the dissociation energy. The thermal stability of the multicomponent crystals was investigated by the DSC and TG methods. The pH-solubility behavior of the cocrystals was investigated at different pH values using eutectic concentrations of the components. Three out of five co-crystals were found to be more soluble than the parent TDZH at low pH values (≈2.0). However, cocrystallization significantly alters the solubility-pH dependence of TDZH, increasing the compound solubility at neutral pH values.