For what it's worth, I suspect your topic belongs here: http://www.flyertalk.com/forum/travelbuzz-176/ as it has indeed nothing to do with FB.

For what it's worth, I have never been able to get a second passport while keeping the old one valid despite going through multiple attempts (long term visas, etc).

Your example of Israel + an Arab country is a total no go: Israel will let you in with stamps from anywhere, and they themselves do not stamp passports any more (you receive separate codebar cards) so no reason why it should lead to a bar in the likes or Iran and Saudi Arabia either. However, Abkhazia stamps may be considered incompatible with Georgia.