Switch-like activation of the spindle assembly checkpoint (SAC) is critical for accurate chromosome segregation and for cell division in a timely manner. To determine the mechanisms that achieve this, we engineered an ectopic, kinetochore-independent SAC activator: the "eSAC." The eSAC stimulates SAC signaling by artificially dimerizing Mps1 kinase domain and a cytosolic KNL1 phosphodomain, the kinetochore signaling scaffold. By exploiting variable eSAC expression in a cell population, we defined the dependence of the eSAC-induced mitotic delay on eSAC concentration in a cell to reveal the dose-response behavior of the core signaling cascade of the SAC. These quantitative analyses and subsequent mathematical modeling of the dose-response data uncover two crucial properties of the core SAC signaling cascade: (1) a cellular limit on the maximum anaphase-inhibitory signal that the cascade can generate due to the limited supply of SAC proteins and (2) the ability of the KNL1 phosphodomain to produce the anaphase-inhibitory signal synergistically, when it recruits multiple SAC proteins simultaneously. We propose that these properties together achieve inverse, non-linear scaling between the signal output per kinetochore and the number of signaling kinetochores. When the number of kinetochores is low, synergistic signaling by KNL1 enables each kinetochore to produce a disproportionately strong signal output. However, when many kinetochores signal concurrently, they compete for a limited supply of SAC proteins. This frustrates synergistic signaling and lowers their signal output. Thus, the signaling activity of unattached kinetochores will adapt to the changing number of signaling kinetochores to enable the SAC to approximate switch-like behavior.