Honestly I only played the first X-com and the more recent russian developed UFO: extra terrestrials (not really X-com, but damn close)...and its been a long while since I played those, so you probably know a lot more about the setting and such than I do. I'm not looking for a game that is too strictly focused on the X-com story, but rather loosly based on it. We could even invent a few new aliens to mix things up a bit.
As far as plot ideas...most of the general ideas I have for the story are laid out in the opening post. The first part of the story would take place on earth (or whatever colonized planet we decide on) Our two characters, fresh out of training get assigned to the same squad. On their first mission things go bad, they are the only two to make it back and since then are rather close, depending on one another. As time goes on their relationship grows....eventually one gets captured, there's likely to be some alien experiments, maybe some probing or attempts at cross breeding, depends on what you're willing to do and/or read about.
I'm sure you have ideas of your own, so shoot me a PM and we can discuss them.