Despite new antivirals are being approved against SARS-CoV-2 they suffer from significant constraints and are not indicated for hospitalized patients, who are left with few antiviral options. Repurposed drugs have previously shown controversial clinical results and it remains difficult to understand why certain trials delivered positive results and other trials failed. Our manuscript contributes to explaining the puzzle: this might have been caused by a suboptimal drug exposure and, consequently, an incomplete virus suppression, also because the drugs have mostly been used as add-on monotherapies. As with other viruses (e.g., HIV and HCV) identifying synergistic combinations among such drugs could overcome monotherapy-related limitations. In a cell culture model for SARS-CoV-2 infection the following stringent criteria were adopted to assess drug combinations: 1) identify robust, synergistic antiviral activity with no increase in cytotoxicity, 2) identify the lowest drug concentration inhibiting the virus by 100% (LIC100) and 3) understand whether the LIC100 could be reached in the lung at clinically indicated drug doses. Among several combinations tested, remdesivir with either azithromycin or ivermectin synergistically increased the antiviral activity with no increase in cytotoxicity, improving the therapeutic index and lowering the LIC100 of every one of the drugs to levels that are expected to be achievable and maintained in the lung for a therapeutically relevant period of time. These results are consistent with recent clinical observations showing that intensive care unit admission was significantly delayed by the combination of AZI and RDV, but not by RDV alone, and could have immediate implications for the treatment of hospitalized patients with COVID-19 as the proposed "drug cocktails" should have antiviral activity against present and future SARS-CoV-2 variants without significant overlapping toxicity, while minimizing the onset of drug resistance. Our results also provide a validated methodology to help sort out which combination of drugs are most likely to be efficacious in vivo, based on their in vitro activity, potential synergy and PK profiles.