IMO, and the opinion of the Church, is to view the "body & blood" in terms of the Greek concept of "essence", and this influence, especially Aristotle, was very strong within the Church's theology. Let me use an example.
Let's say that the reader doesn't know what a "car" is and (s)he asks me to explain. So, what I do is to mention various parts: the body, the engine, the wheels, and all the other various parts, but then I stop there. After all, I covered every single part. But then the reader looks mystified and says "But what is it used for?".
So, even though I covered all it's parts, I still didn't explain its "essence". The Eucharist can and should be viewed in that latter manner, namely that it's more than just a sum of its parts. Or, to put it another way, it's not just what the composition of the bread & wine is but also it's what its "essence" is: the body and blood of Christ.