Many immunoreceptors have cytoplasmic domains that are intrinsically disordered (i.e., have high configurational entropy), have multiple sites of posttranslational modification (e.g., tyrosine phosphorylation), and participate in nonlinear signaling pathways (e.g., exhibiting switch-like behavior). Several hypotheses to explain the origin of these nonlinearities fall under the broad hypothesis that modification at one site changes the immunoreceptor’s entropy, which in turn changes further modification dynamics. Here, we use coarse-grain simulation to study three scenarios, all related to the chains that constitute the T cell receptor (TCR). We find that first, if phosphorylation induces local changes in the flexibility of the TCR ζ-chain, this naturally leads to rate enhancements and cooperativity. Second, we find that TCR CD3ɛ can provide a switch by modulating its residence in the plasma membrane. By constraining our model to be consistent with the previous observation that both basic residues and phosphorylation control membrane residence, we find that there is only a moderate rate enhancement of 10% between first and subsequent phosphorylation events. Third, we find that volume constraints do not limit the number of ZAP70s that can bind the TCR but that entropic penalties lead to a 200-fold decrease in binding rate by the seventh ZAP70, potentially explaining the observation that each TCR has around six ZAP70 molecules bound after receptor triggering. In all three scenarios, our results demonstrate that phenomena that change an immunoreceptor chain’s entropy (stiffening, confinement to a membrane, and multiple simultaneous binding) can lead to nonlinearities (rate enhancement, switching, and negative cooperativity) in how the receptor participates in signaling. These polymer-entropy-driven nonlinearities may augment the nonlinearities that arise from, e.g., kinetic proofreading and cluster formation. They also suggest different design strategies for engineered receptors, e.g., whether or not to put signaling modules on one chain or multiple clustered chains.