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Tyrosine kinase receptor (RTK) ligation and dimerization is a key mechanism for translating external cell stimuli into internal signaling events. This process is critical to several key cell and physiological processes, such as in angiogenesis and embryogenesis, among others. While modulating RTK activation is a promising therapeutic target, RTK signaling axes have been shown to involve complicated interactions between ligands and receptors both within and across different protein families. In angiogenesis, for example, several signaling protein families, including vascular endothelial growth factors and platelet-derived growth factors, exhibit significant cross-family interactions that can influence pathway activation. Computational approaches can provide key insight to detangle these signaling pathways but have been limited by the sparse knowledge of these cross-family interactions. Here, we present a framework for studying known and potential non-canonical interactions. We constructed generalized models of RTK ligation and dimerization for systems of two, three and four receptor types and different degrees of cross-family ligation. Across each model, we developed parameter-space maps that fully determine relative pathway activation for any set of ligand-receptor binding constants, ligand concentrations and receptor concentrations. Therefore, our generalized models serve as a powerful reference tool for predicting not only known ligand: Receptor axes but also how unknown interactions could alter signaling dimerization patterns. Accordingly, it will drive the exploration of cross-family interactions and help guide therapeutic developments across processes like cancer and cardiovascular diseases, which depend on RTK-mediated signaling.