As far as I know there is no regulatory limit to the "number of instructions" that can be given in one transmission. The most lengthy set of instructions from ATC is typically an IFR clearance, where a pilot is given a clearance limit, a route to follow (which can in itself be many instructions), maybe a departure heading and altitude, a departure control frequency, a squawk code, maybe a void time, and possibly a number of other things, all in a single transmission. But the pilot is prepared for this (he just ask for it!), and is usually on the ground with pen and paper in hand ready to copy it all down.
I think most controllers will limit the number of instructions they give pilots once they are airborne to three or four at the most. They don't want to have to repeat themselves either, so there is no point in overrunning a pilot's short-term memory! Something like a heading, altitude and speed change is just normal and expected and not a problem in a single transmission. For something more complicated, like an airborne full-route clearance, a controller would typically say something like "Lear 2 8 Bravo Hotel, I have a reroute for you, advise when ready to copy" - and that's your signal to get your pen ready to copy a bunch of stuff!