Join Date: Nov 2005
Location: SIN / CNX / SFO
Programs: UA GS, SQ PPS, Hyatt Globalist, Marriott Titanium, Hilton Diamond, Accor Gold
Posts: 1,253
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.