Originally Posted by
Scifience
Definitely possible! In fact, I'd imagine that a significant portion of this site's membership has multiple valid visas at any given time. I have six at present...
Many countries prohibit having multiple valid visas for their country at a time (e.g. a tourist visa and a work visa or two unused single-entry visas), so perhaps this is what you had heard.
HK and KSA at the same time is no issue at all.
This. I've had multiple visas in my passport at once more than once. Once I even had two multiple-entry visas for China in my passport at the same time. When we hit immigration the older of the two got cancelled but it was basically moot at that point anyway, it would have expired in a few minutes.