Climate pollutants and air-quality pollutants would not be part of the same index, except perhaps total "economic costs". Climate pollutants can be lumped into a CO2-equivalent value, which relies on the residence time and warming potential.
For criteria air pollutants that are regularly monitored (NO2, CO, O3, PM2.5, SO2), EPA uses a method which reports the air quality index for the worst pollutant. For toxic air pollutants, air quality agencies have typically done the same thing, just pick the worst one.
Health based standards are usually expressed in terms of the cancer or mortality probability for a single pollutant. However, cumulative and combined exposure to multiple air pollutants can have more negative health effects than just "the worst one", or even worse than the simple additive effects across all pollutants. It is very difficult to come up with a cumulative and combined health metric because most health studies don't have that type of robust information. But, we do know that the health effects are compounded when their are multiple stressors. In order to calculate the cumulative health impacts of multiple air pollutants, some people use BenMAP, which I believe incorporates the Cox proportional hazards model to make the calculation.
The Cox proportional-hazards model (Cox, 1972) is essentially a [statistical] regression model commonly used in medical research for investigating the association between the survival time of patients and one or more predictor variables.
You might find other useful models at the EPA's Air: Fate, Exposure and Risk Analysis site.
Environmental groups are pushing air quality agencies to now consider cumulative exposure when permitting facilities, especially under the environmental justice context. See Oregon's Cumulative Health Risk pilot study for toxics, as an example.