Originally Posted by UA-NYC

I read it as the OP has separate one way tickets from/to the US, something like PHL-XXX-IST-ATH / TLV-XXX-PHL, and would like to somehow make his IST connection a 24+ hour stopover.

OP - if this is the case, this is very doable...your itinerary would look like this:

PHL-XXX-IST (stop)
IST-ATH (destination / open jaw)
TLV-XXX-PHL

You may have to play agent roulette to ticket it, but it is legal

Also - you can't just combine your two one-ways...you have to convert one of your one ways to a round-trip, but need to make sure there's availability on all the segments.