I know of no absolute rule, and so would depend upon the proximity principle to produce something that hopefully read well:
You cannot demand nor expect that he will read the appendices.
You cannot expect nor demand that he read the appendices.
The proximity principle is more an observation than a rule - in cases where there is a conflict of agreement because of two or more words being joined by a conjunction that would require a different number, mood, etc. in what follows, then make the agreement happen with those words that are closer to each other and it will tend to sound correct whether it is or not!
However, if what was added could be read as a parenthetical clause, then I would treat it as if it could be omitted:
You cannot demand, nor expect, that he read the appendices.
You cannot expect, nor demand, that he will read the appendices.
Again though, I know of no absolute rule.