Cell fate decisions during embryonic development and tumorigenesis pose a major research challenge in modern developmental and cancer biology. Binary cell fate decisions are usually regulated by gene circuits incorporating either classical toggle switches with two mutually inhibiting transcription factor (TF) genes or chimera toggle switches with a mutually inhibiting pair of microRNA (miRNA) and TF gene. These circuits can explain binary cell fate decisions. Importantly, intermediate cell types can exist during the differentiation of both stem cells and cancer cells. It has been shown that TF-TF self-activating toggle switches (SATS) can have coexistence of three metastable states (tristability), yet the role of chimera toggle switches in opening these additional states remains elusive. Here we present a generalized framework for both the TF-TF SATS and miRNA-TF chimera SATS, starting from the TF-promoter and miRNA-mRNA binding/unbinding dynamics. We show that the chimera SATSs can also have tristability. We demonstrate that the dynamics of miRNA-TF SATS is qualitatively different from that of the TF-TF SATS because the nonlinear effects of translational silencing by miRNA are distinct from those of transcriptional repression. We discuss the possible relevance of these findings to fate decisions by cancer cells.