Climate targets are designed to inform policies that would limit the magnitude and impacts of climate change caused by anthropogenic emissions of greenhouse gases and other substances. The target that is currently recognized by most world governments places a limit of two degrees Celsius on the global mean warming since preindustrial times. This would require large sustained reductions in carbon dioxide emissions during the twenty-first century and beyond. Such a global temperature target, however, is not sufficient to control many other quantities, such as transient sea level rise, ocean acidification and net primary production on land. Here, using an Earth system model of intermediate complexity (EMIC) in an observation-informed Bayesian approach, we show that allowable carbon emissions are substantially reduced when multiple climate targets are set. We take into account uncertainties in physical and carbon cycle model parameters, radiative efficiencies, climate sensitivity and carbon cycle feedbacks along with a large set of observational constraints. Within this framework, we explore a broad range of economically feasible greenhouse gas scenarios from the integrated assessment community to determine the likelihood of meeting a combination of specific global and regional targets under various assumptions. For any given likelihood of meeting a set of such targets, the allowable cumulative emissions are greatly reduced from those inferred from the temperature target alone. Therefore, temperature targets alone are unable to comprehensively limit the risks from anthropogenic emissions.