grammar - What type of word allows raising?

I've come across a comment in “it seems” vs. “it seems that” and I am uncertain as to what type of word allows raising.

It's not necessary (though it's almost always possible) for any complement clause (no matter what it expresses), except when the complement clause comes at the beginning of the sentence. (BTW, the clause "The word that is not necessary to be there" is ungrammatical, since necessary does not allow A-Raising.) – John Lawler Jul 27 '14 at 17:58