Well, Pat gave me ideas so I looked at RT MEM/CAI and we could do it all on KLM. How much of a jump is it from AMM to CAI? (edit; I see Egyptair does it in 25 minutes, Royal Jordanian takes an hour and a half, not bad). What date are you using for your return? We'd be spending 10 hours in Amsterdam on the way to Cairo, so would have to back up a day on departure. I think.
Betty, the Royal Jordanian flight was from Amman to Amsterdam. If we do Cairo RT, they wouldn't be in the picture anymore.