Elucidating the design principles of regulatory networks driving cellular decision-making has important implications in understanding cell differentiation and guiding the design of synthetic circuits. Mutually repressing feedback loops between 'master regulators' of cell-fates can exhibit multistable dynamics, thus enabling multiple 'single-positive' phenotypes: (high A, low B) and (low A, high B) for a toggle switch, and (high A, low B, low C), (low A, high B, low C) and (low A, low B, high C) for a toggle triad. However, the dynamics of these two network motifs has been interrogated in isolation in silico, but in vitro and in vivo, they often operate while embedded in larger regulatory networks. Here, we embed these network motifs in complex larger networks of varying sizes and connectivity and identify conditions under which these motifs maintain their canonical dynamical behavior, thus identifying hallmarks of their functional resilience. We show that the in-degree of a motif - defined as the number of incoming edges onto a motif - determines its functional properties. For a smaller in-degree, the functional traits for both these motifs (bimodality, pairwise correlation coefficient(s), and the frequency of 'single-positive' phenotypes) are largely conserved, but increasing the in-degree can lead to a divergence from their stand-alone behaviors. These observations offer insights into design principles of biological networks containing these network motifs, as well as help devise optimal strategies for integration of these motifs into larger synthetic networks.