What Does It Mean to Say "being is intrinsically diverse"?

Being "actually & implicitly comprehends" its differences.

It is not the result of an "abstractio totalis", a "universal known in the most general & least determinate fashion", an empty container we dump other things into (this is the sub-concept of being logic works with in analyzing second intentions... a confusion between the two has led to people saying the argument we are discussing doesn't work; see Novak on 'Aporia Generis').

Being is instead "trans-specific, transgeneric, trandindividual, transcategorical", a "variable enveloping an actual multiplicity": like a "liquid crytsal" wherein other forms are already bound up and actual. Maritain calls it a "superuniversal"; it differs from a genus "not only because it has greater amplitude but because it is not, like a genus, simply one - it is polyvalent, envelops an actual multiplicity". It is "the highest form of all, what makes all other things actual, even their forms".

So we can't think of any one being without "rendering present to the mind some of the essentially other ways in which [being] is realized". When you think of black, insofar as black is a [mode of] being, you are also laterally considering red.

We know this because (as you say) being can't be extrinsically diversified. It's differences can't be extrinsic; so if "black" was being to the exclusion of red, red would be nothing. Goes way back to Aristotle's response to Parmenides: being is either intrinsically diversified (as into act/potency & the various special modes that result from the distinction) or difference is unreal.

So, insofar as all things are participatory modes or "determinations" of being, they can't be added to it.