Like other neurodegenerative diseases, Alzheimer Disease (AD) has a prominent inflammatory component mediated by brain microglia. Reducing microglial inflammation could potentially halt or at least slow the neurodegenerative process. A major challenge in the development of treatments targeting brain inflammation is the sheer complexity of the molecular mechanisms that determine whether microglia become inflammatory or take on a more neuroprotective phenotype. The process is highly multifactorial, raising the possibility that a multi-target/multi-drug strategy could be more effective than conventional monotherapy. This study takes a computational approach in finding combinations of approved drugs that are potentially more effective than single drugs in reducing microglial inflammation in AD. This novel approach exploits the distinct advantages of two different computer programming languages, one imperative and the other declarative. Existing programs written in both languages implement the same model of microglial behavior, and the input/output relationships of both programs agree with each other and with data on microglia over an extensive test battery. Here the imperative program is used efficiently to screen the model for the most efficacious combinations of 10 drugs, while the declarative program is used to analyze in detail the mechanisms of action of the most efficacious combinations. Of the 1024 possible drug combinations, the simulated screen identifies only 7 that are able to move simulated microglia at least 50% of the way from a neurotoxic to a neuroprotective phenotype. Subsequent analysis shows that of the 7 most efficacious combinations, 2 stand out as superior both in strength and reliability. The model offers many experimentally testable and therapeutically relevant predictions concerning effective drug combinations and their mechanisms of action.