About that, I'm not sure the "one additional" phrasing matters. "If X happens, you can do Y one additional time" doesn't mean you can't do Y again if X happens again. Or in other words, if game text says "Each time a companion exerts, you may exert that companion one additional time," I'd argue that you can keep exerting that companion.
Though as mentioned, I think the limit *is* handled--just in another way.