In the category of functional low-affinity interactions, small ligands may interact with multiple protein sites in a highly degenerate manner. Better conceived as a partition phenomenon at the molecular interface of proteins, such low-affinity interactions appear to be hidden to our current experimental resolution making their structural and functional characterization difficult in the low concentration regime of physiological processes. Characterization of the partition phenomenon under higher chemical forces could be a relevant strategy to tackle the problem provided the results can be scaled back to the low concentration range. Far from being trivial, such scaling demands a concentration-dependent understanding of self-interactions of the ligands, structural perturbations of the protein, among other molecular effects. Accordingly, we elaborate a novel and detailed concentration-dependent thermodynamic analysis of the partition process of small ligands aiming at characterizing the stability and structure of the dilute phenomenon from high concentrations. In analogy to an "aggregate" binding constant of a small molecule over multiple sites of a protein receptor, the model defines the stability of the process as a macroscopic equilibrium constant for the partition number of ligands that can be used to analyze biochemical and functional data of two-component systems driven by low-affinity interactions. Acquisition of such modeling-based structural information is expected to be highly welcome by revealing more traceable protein-binding spots for non-specific ligands.