Ah, crumbs, they've discovered my weakness. Drawing lines.
Mainly because, as certain Golden Horde references have established, it's all very well saying "Europe, not Asia" if Asia doesn't plan on staying put. Equally, it's not much use my saying X amount of Asian influence is reasonable, because said X amount will undoubtedly have been influenced by things further East, at which point we have to start asking how far Far Eastern is too far Far Eastern? And that would get... confusing.
The present rule ("European and Mediterranean") is questionable and flimsy, but this is intentional.
It ensures that the creators of cultures which are borderline acceptable have to pitch their idea at us (not necessarily in full) before assuming that the rules give them the right to go on their merry way. Typically, if said elevator pitch smells a lot like someone who just wants Mongol bows or Russian vodka or some other perk, or someone whose only knowledge of Arabian culture is Disney's Aladdin, odds are you're not in for a happy conversation.
If, however, it sounds like you know vaguely what you're talking about, and if you can respond to questions about how it would mesh with the current cultures of Altera, and if it's clear you've used your imagination as well as Wikipedia, you have a fighting chance at gaining permission. However, it should be noted that the further East you're looking for inspiration, the less likely you will be allowed to write/play the culture, and the actual Far East is out of the question for reasons which have been well-articulated by Cap's forum alerts.
The safer bets for outside-the-box cultures, however, are those which match the "Mediterranean" specification, such as long-term cultures of the Near East/Asia Minor, and/or the North coast of Africa. As the Byzantine Empire was chilling in the vicinity for a ridiculously extensive period of time, that's a good example of a reasonable source.