Since Vatican II, in an attempt bring the Eastern Orthodox Churches to Rome, the Roman Catholic Church has adopted the Epiclesis into their liturgy. What does this do the the theology of sacrifice? Before we get to that, for those in our audience who are unaware, let's explain the distinction in Eastern and Western consecration theology.
The Eastern Church and the Western Church have historically disagreed with how the bread and wine become the body and blood of Jesus. According to the East, the Holy Spirit does it when you pray for it to do so. This happens when the Priest says the Eucharistic prayer or Epiclesis. The Eucharistic prayer, combined with the total action of offering, giving and receiving brings about the real presence. This was pretty much what people thought as far as we can tell in the early Church from about the 2nd century to the 4th or 5th. Johann Gerhard in Lutheranism actually endorsed the view that the Epiclesis did it(unfortunately, and strangely in light of the fact that Luther removed the Eucharist prayer from the liturgy). The West, St. Ambrose, developed a theology of the moment of consecration. In other words, when the Priest actually says the words of institution, then it becomes the body and blood of Christ. Lutherans more or less buy into this, that is, the idea that the elements are consecrated by the word of Jesus' promise and not a prayer that Jesus never commanded, even if differences between consecrationists and distributionists still persist (I'm pretty staunchly a consecrationist, but more on that later).
After Vatican II, as I mentioned, the Catholics in order to get the Orthodox back with them re-wrote the liturgy and made the idea of the Epiclesis the thing which transformed the elements. Of course their was an Epiclesis before, but it was the words of instituion which were understood to make the difference. Now that the Epiclesis is back as the catalyst for the real presence, this means a kind of double consecration of the elements and bizzarely long liturgy. In any case, it seems to me that it also means that a new layer of sacrifice and human initiative was actually add to their doctrine of the Eucharist. Let me explain.
Listening to the liturgy this is what you get: Priest tells God (God is always being addressed BTW- the congregation aren't really even addressed with the words of institution, God the Father is!) that he's brought the elements of bread and wine and that they're a kind of offering that the Priest and apparently the congregation through the Priest are also making. Why God is supposed to be interested in this (especially because he did not sanction any such offering and we know how that has a tendency of turning out in the Bible!) is not entirely clear. So, there's the first sacrifice. This wasn't in the pre-Vatican II liturgies. Then the next stage. Because we come and offer these element to God, God is supposed to now send his Holy Spirit on them and make them the body and blood of Christ. Now, let's be fair, it doesn't say anything about meriting this by the offering and I'm absolutely certain that if you talked to a Catholic theologian that he'd say that no merit is involved in get the Holy Ghost to come and do this. But here's the deal: It creates a situation were the divine-human relationship enacted by the Eucharist is a matter of human initiative and human movement towards God through an initial act of sacrifice, that is, an offering the Eucharistic elements.
Now that the elements have been transformed into the body and blood of Christ, the Priest speaks the words of institution to God the Father (for some reason that is unclear) and then offers up the congregation with Christ by their prayer and by their participation in the elements. Here's a really interesting aspect that changed with Vatican II. Before then, Trent and Aquinas had stated that the sacrifice of the Mass was identical with that of the cross, but how they didn't know how. The 20th century German Monk Odo Casel argued (based on his belief that Christianity was an Jewish version of the Greek Mystery cults) that time and space stops and we are transported back in time to the crucifixion so that we can participate in it. This then got into Vatican II. So, the congregation is capable of going back in time and participating in Christ's redemptive act as one person with him. This is sacrifice number two.
Many liberal Lutherans have argued that Vatican II made Catholicism acceptable enough to entertain fellowship again. What I find interesting here is that the opposite is actually the case. Catholicism has in a sense simply doubled up on the theology that we found so problematic in the 16th century.