Question about stopovers
 

Last year my husband and I were bumped from a JFK-CDG flight and nicely compensated with a coupon for an international flight. We will be flying to Egypt on this voucher in late December, returning mid-January. I was wondering if it is possible to arrange for a stopover in Paris on the way back from Cairo? We might even consider paying for it. Does anybody have any suggestions as to the approach we should take with TWA, or with American, when asking about this? Has anyone done it before?
All your assistance is much appreciated. Thank you in advance.

You'll be able to take a stopover, but it will cost you.

If you're leaving in late december (after 16Dec) the cheapeast TW or AA fare JFK/CAI is $1400. However, it doesn't allow for stopovers. The cheapest TW or AA fare that I can find that allows for stopovers in late december is a $1878 fare, which allows for a single stop-over for an additional cost of $100.

Roughly, this means you can go JFK-CAI and then CAI-JFK for about $1410USD with taxes, or JFK-PAR, PAR-CAI, CAI-JFK for about $1988USD.

A much cheaper alternative would be to buy one set of tickets JFK-CDG-JFK, which in late december price out under $400, and then another set of tickets CDG-CAI-CDG, which for late december are under $500 for major carriers. This gets you the entire itinerary for under $1,000. It also means you can, should you chose, stop-over in Paris (or possibly another European city) in both directions...

The downside is that you won't end up with AAdvantage or Aviators points for the CDG/CAI legs because the BA fare for that market is $700, more than $200 over what it would cost on AF/LH/SR. However, even if you did it on BA to get AAdvantage miles, the total cost would still be under $1300/person versus $1988/person using the JFK-CAI (return) fare.

Thank you so much for your very thorough reply. Unfortunately, it made me realize that I hadn't been clear enough in the first place. So I'll try again:
We have a free TWA voucher for JFK-Cairo-JFK. It is compensation for a "bump" last March and is already ticketed. What strategy can I use, provided there is one, to get this changed to JFK-Cairo-CDG-JFK? Can I get it at no cost (given the voucher) or will I have to pay?
Thanks again for being so helpful. This list is great!

No, you will not be able to do that since TWA nor AA flies CDG-CAI.

Greg