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Bivalency confers several concentration-dependent phenomena, including avidity, competitive exchange and multi-site competitive exchange. Since these concepts are crucial for a wide variety of topics in cell and molecular biology, their extension, modification and/or re-purposing is also increasingly important for the design and construction of de-novo synthetic systems at the nanoscale. In this context, we draw upon classical techniques of statistical physics to revisit bivalency, highlighting that receptor site geometry offers a design modality independent of the chemistry of the individual binding interfaces themselves. Recasting the problem in terms of many-body coordination, we explore extended, translationally-invariant chains and lattices of receptor sites. This not only brings clarity to behaviours associated with simpler motifs, but also enables us to distil core principles for the rational design of concentration-dependent kinetics in synthetic soft-systems, which centre on the notion of geometric frustration. In doing so, we also reveal the possibility of other tunable spatio-temporal features, such as correlation lengths, mean-squared displacements and percolation-like transitions.