Suppose I say to Bill: "Make all of your papers be between two and four pages." Bill hands in an eight page paper for his first assignment. I rebuke him and he apologizes. He then hands in another eight page paper for his second. When I rebuke him, he says: "You told me to bring it about that all my papers be between two and four pages. With my first paper I ensured that the proposition that all my papers are between two and four pages is false. Sorry! By the time of my second paper, it was too late to undo this: no matter what length of paper I wrote, that proposition would still be false. So I might as well write the length that I like."
Bill's mistake was thinking that the content of my command was the proposition that all his papers be between two and four pages. I didn't command that proposition. Rather, I commanded distributively of each of his papers that it be between two and four pages.
This means that we should not analyze my speech act as having a propositional content plus an illocutionary force. The content of the speech act wasn't a proposition, but something else. Perhaps the content of the speech act was an ordered pair of properties, the property P of being one of Bill's papers, and the property L of being between two and four pages in length. And the illocutionary force was of something one might call distributive command. Successful distributive command in respect of a pair of properties P and L creates for each instance x of P a reason to make x have L.
There are, I think, assertion-like speech acts that also have such a non-propositional content. For instance, assertoric endorsement. A paradigm case: I endorse what you are about to assert. The content of assertoric endorsement is a property which is supposed to be had by one or more propositions—say, the property of being soon asserted by you—and when successful, the assertoric endorsement makes you stand behind each of these propositions as if you asserted it. This kind of assertoric endorsement is distributive.
I wish I knew what kinds of entities can be contents of speech acts. The above suggests that some speech acts have propositions as contents, some have pairs of properties, some have single properties. There must be many other options.