Global change driven by anthropogenic carbon emissions is altering ecosystems at unprecedented rates, especially coral reefs, whose symbiosis with algal symbionts is particularly vulnerable to increasing ocean temperatures and altered carbonate chemistry. Here, we assess the physiological responses of three Caribbean coral (animal host + algal symbiont) species from an inshore and offshore reef environment after exposure to simulated ocean warming (28, 31°C), acidification (300–3290 μatm), and the combination of stressors for 93 days. We used multidimensional analyses to assess how a variety of coral physiological parameters respond to ocean acidification and warming. Our results demonstrate reductions in coral health inSiderastrea sidereaandPorites astreoidesin response to projected ocean acidification, while future warming elicited severe declines inPseudodiploria strigosa. OffshoreS.sidereafragments exhibited higher physiological plasticity than inshore counterparts, suggesting that this offshore population was more susceptible to changing conditions. There were no plasticity differences inP.strigosaandP.astreoidesbetween natal reef environments, however, temperature evoked stronger responses in both species. Interestingly, while each species exhibited unique physiological responses to ocean acidification and warming, when data from all three species are modelled together, convergent stress responses to these conditions are observed, highlighting the overall sensitivities of tropical corals to these stressors. Our results demonstrate that while ocean warming is a severe acute stressor that will have dire consequences for coral reefs globally, chronic exposure to acidification may also impact coral physiology to a greater extent in some species than previously assumed. Further, our study identifiesS.sidereaandP.astreoidesas potential ‘winners’ on future Caribbean coral reefs due to their resilience under projected global change stressors, whileP.strigosawill likely be a ‘loser’ due to their sensitivity to thermal stress events. Together, these species-specific responses to global change we observe will likely manifest in altered Caribbean reef assemblages in the future.