Originally Posted by
mc510
Or, to describe my ignorance a little differently, I'm not sure if free stopovers are still a common feature on international flights (my recollection being that they were, quite a few years back when I traveled more).
They are, it's just that (especially on ITA if you select "cheapest") nowadays the lowest Y fares are so ridiculously restricted that stopovers might indeed be almost banned.
An interesting stopover that is available at the moment is in Portugal with TAP, where you get up to 5 days for free. Maybe it could be an idea to use that as ATH-LIS/OPO-XXX, where XXX is your gateway back to SFO.
Also, when searching on ITA, try using the multi city tool instead of forcing connection points. It should show you only fares that allow stopovers. I just found this, randomly:
