At Exxon, our lube planner would mix base stocks, 5 grade into 10 grade, 30 grade into 10 grade, etc. This is to make viscosity, flash point, boiling point, etc. on a particular base stock. It wasn't done a lot, but there certainly weren't any rules against it. We didn't go mixing huge amounts of 30 and 10 grade to made a 20 grade, for instance. Standard dino oil is a whole spread of molecules but with the average generally giving it the desired vis grade and boiling point. I've put together lube oil blending programs that mix all the properties. We had NO REASON from a research or engineering standpoint to prohibit what went into the blends, as long as the product was on spec. We generally fractionated the oils from the stills to make specifications as carefully as we could, to eliminate blending, because running more narrow cuts franctions through our dewaxing plants made them run better, and we generally didn't want to do blending in the end. However, we had no problem with doing a little end blending to make specifications.
Do not mix dino with synthetic. Otherwise, you've wasted your money that you paid extra to get the very pure synthetic. However, if it's a choice of an engine or gear box running out of oil vs. mixing, then mixing is fine.
A couple of times, I've mixed 15w50 with 5w30 to get 10w40 grade for my old Benz. Lately, I've been able to get 5w40 or 0w40; so this is what I use in it.
Ralph