Interconnected feedback loops are prevalent across biological mechanisms including cell fate transitions enabled by epigenetic mechanisms driving phenotypic plasticity of carcinoma cells. However, the operating principles of these networks remain largely unexplored. Here, we identify numerous coupled feedback loops driving phenotypic transition in cancers and CD4+ T cell lineage decisions. These networks have three generic structures, serial type (ST), hub type (HT), and cyclic, which we discover to be the hallmarks of lower- and higher-order dynamics. While networks having ST or cyclic topology exhibit multiple alternative states, those having HT topology enable at most two states. We also show that topologically distinct networks with equal node or loop count exhibit different steady-state distributions, highlighting the crucial influence of network structure on emergent dynamics. Irrespective of the topology, networks with autoregulated genes exhibit multiple states thereby liberating network dynamics from absolute topological control. Finally, we identify precise gene interaction targets to restrict the multistable network dynamics to a unique state. Our results thus reveal design principles of coupled feedback loops in enabling multiple alternative states while also identifying perturbations to restrict it. These findings can serve as crucial inputs to comprehend multi-fate decisions of cells and phenotypic plasticity in carcinomas.