Alphaviruses such as Venezuelan equine encephalitis virus (VEEV) are associated with a significant burden of disease, disability, death, and medical expenditures. No oral antiviral drugs are available for this virus family. We have shown that combinations of oral nucleoside analogs approved for other virus families confer synergistic suppression of alphaviruses. However, not all nucleoside analogs were effective against VEEV. Here, we explored additional directly acting antiviral (DAA) drug combinations for their efficacy against VEEV in vitro. We also tested thirteen drugs approved for non-viral indications that have been shown potential as host targeting antiviral (HTA) drugs. We confirm the strong antiviral potency of ML-336, a previously described oral DAA that is thought to inhibit VEEV non-structural protein-protein interactions to suppress viral RNA synthesis. Combining ML-336 with nucleoside analogs favipiravir (FAV) or molnupiravir (MPV) confers synergistic suppression of VEEV TC83 in human skin fibroblasts and liver cells. Of thirteen HTA drugs screened, only the pyrimidine biosynthesis inhibitor brequinar (BRQ) suppressed VEEV TC83 in human skin fibroblasts. BRQ inhibition of VEEV in these cells was variable and this variability was not abated by synchronizing the cell cycle through serum starvation or by synchronizing infection by using high multiplicities of infection. BRQ did not inhibit VEEV TC83 in human liver cell cultures, but BRQ did suppress Sindbis virus (SINV) in these cells. The results emphasize the challenge and cell type variability associated with putative HTA drugs and further support the potential of all-DAA and DAA + HTA drug combinations against emerging and re-emerging alphaviruses.