Vitamin C seems to be what most animals on this planet use as general anti-viral. It also seems it works in humans in mega dozes and/or IV.
In any case "general antiviral" seems to be even worst thing then general antibiotic. Most of bacteria / viruses are commensal, you don't really want to disturb that. For example, bacteriophage viruses are now known to handle some of the 100% resistant bacteria in a matter of days.
IMO, the system is so complex that you should only support the crew that know how to handle that - i.e. your immune system - by providing resources they need (vitamins etc.) and avoid things detrimental for them (sugar, tonsillectomy etc.).
In any case "general antiviral" seems to be even worst thing then general antibiotic. Most of bacteria / viruses are commensal, you don't really want to disturb that. For example, bacteriophage viruses are now known to handle some of the 100% resistant bacteria in a matter of days.
IMO, the system is so complex that you should only support the crew that know how to handle that - i.e. your immune system - by providing resources they need (vitamins etc.) and avoid things detrimental for them (sugar, tonsillectomy etc.).