Intermolecular interactions, in particular hydrogen bonds, play a key role in crystal engineering. The ability to form hydrogen bonds of various types and strengths causes competition between supramolecular synthons in pharmaceutical multicomponent crystals. In this work, we investigate the influence of positional isomerism on the packing arrangements and the network of hydrogen bonds in multicomponent crystals of the drug riluzole with hydroxyl derivatives of salicylic acid. The supramolecular organization of the riluzole salt containing 2,6-dihydroxybenzoic acid differs from that of the solid forms with 2,4- and 2,5-dihydroxybenzoic acids. Because the second OH group is not at position 6 in the latter crystals, intermolecular charge-assisted hydrogen bonds are formed. According to periodic DFT calculations, the enthalpy of these H-bonds exceeds 30 kJ·mol−1. The positional isomerism appears to have little effect on the enthalpy of the primary supramolecular synthon (65–70 kJ·mol−1), but it does result in the formation of a two-dimensional network of hydrogen bonds and an increase in the overall lattice energy. According to the results of the present study, 2,6-dihydroxybenzoic acid can be treated as a promising counterion for the design of pharmaceutical multicomponent crystals.