Christianity, it has been said, is the greatest story ever told. Some Christian thinkers, like Alvin Plantinga, have gone further and said that Christianity is the greatest story that ever could have been told. In no logically possible world, the suggestion goes, is there a story better than the Christian story of redemption, and the love of God, and the purpose of man, the meaning of life and so on. Now, it seems to me that some Protestants are, now and again, struck by the beauty of the Catholic story of the Church, even if they don’t accept it – meaning that when they come to see the Church, or just glance at the Church, through the lens of the Catholic tapestry of faith, they see a more beautiful picture of her than they do (or even can) through a Protestant lens. The vision of the Catholic Church as one mystical body, or person, and as being the incarnational extension of Jesus’ person, presence and ministry (in all its dimensions, from miracles to forgiving sins, and even to infallibly teaching the truth in a way in principle accessible as such to all men) in the world, is a quite beautiful picture, and it is distinctive of the Catholic (and Orthodox) view(s). If this is so, then Christianity’s being the greatest story possibly told seems to imply that the Catholic and Orthodox vision of the Church is the properly Christian one after all. At least this is the case if what is gained in terms of beauty by this ecclesiology exceeds whatever net cost in beauty it would incur (or necessarily incur), but that seems plausible enough, since it doesn’t seem to be necessary that we sacrifice any of the net beauty of the Christian story in order to make room for the Catholic doctrine of the Church.
Unfortunately this is an argument from beauty, and as with other such arguments from beauty, you either see it or you don’t. It impresses me, but I would not be surprised to find that it does not impress everyone (though I would be very surprised, and even perplexed, if it did not impress somebody who is both Christian and who really understood the Catholic/Orthodox/etc. vision of the Church). In any case, it is at least some kind of argument for the truth of Catholicism (and Eastern Orthodoxy, and Oriental Orthodoxy, and other autocephalous yet genuinely Apostolic forms of Christianity) which appeals to intuitions which the Protestant shares (or in any case should share, I think) with Catholics (etc.).
As a final note, I think we can both expand and contract this argument somewhat. First, we can contract this argument and say something similar about the doctrine of the Papacy, since it offers to the Christian what is missing in the Eastern Orthodox, Oriental Orthodox, and other such views of the Church; namely, a ministry by which the Church can unambiguously manifest both her unity and her orthodoxy. We might even go further, if we were feeling particularly ambitious, and draw on Thomas Aquinas’ argument in the Contra Errores Graecorum (according to which the Eastern Orthodox ecclesiology takes a wrong turn precisely where it does because it takes a wrong turn in its doctrine of the Trinity insofar as it forgets the truth of the Filioque clause in the Latin Creed) to argue that insofar as the Filioque renders the doctrine of the Trinity more beautiful than it otherwise would have been, and insofar as our ecclesiology is ultimately a reflection, to some extent, of our doctrine of the Trinity, the Catholic ecclesiology of the Church is a better, fuller and more beautiful reflection of Christian doctrine than the Orthodox ecclesiologies. Second, we can expand this argument outward (in a more ecumenical direction, perhaps) and say that if God exists then it is plausible that he would actualize, to the extent possible, the best story, and this turns into an argument for the Christian story which we might give to the Deist or other non-Christian theists.
 Protestant ecclesiology can allow for the Church to teach without error, but not to teach infallibly (for infallibility is as far from ‘free of error’ as inerrancy is from ‘free of error;’ in both cases it’s not merely that there happens to be no error – as there may happen to be no error in a history book, but that wouldn’t make it inerrant – but that there could not have been any error even in principle precisely because of the nature of the source). Moreover, even if the Protestant could, by some theological acrobatics, make room for the Church to teach infallibly in some sense, and even if those teachings were somehow accessible to all men, the Church would not be able to make her infallibility manifest to all men, and thus she would be unable to present her infallible teachings to man as such (meaning, as ostensibly infallible), since she would only be able to present infallible teachings to all men in such a way that not all men could in principle tell the difference between those of her teachings which are infallible and those teachings, apparently from her, which circulate with the admixture of human error.
 If it doesn’t incur the cost necessarily, then there is a logically possible world in which the Christian story is more beautiful for it, but we have already stated at the outset that the Christian story is maximally beautiful.
 See: James Likoudis, Ending the Byzantine Greek Schism: The 14th C. Apologia of Demetrios Kydones for Unity with Rome and the “Contra Errores Graecorum” of St. Thomas Aquinas. (New Rochelle: Catholics United for the Faith, 1983), 126-189.