One of the main areas of study and research into Roman Catholicism I have engaged in is that of the Mass and related dogmas. For articles interacting with Roman Catholic apologists on the Mass, see:
Responses to Robert Sungenis, Not By Bread Alone (2000/2009)
One interesting area of debate among Catholic theologians relates to whether there is sacrifice in heaven, and how such would relate to the heavenly priesthood of Christ, the ordained priesthood on earth, and the once-for-all nature of Christ's sacrifice. For more, see, "Appendix 6: The Cross, Mass & Christ’s Priesthood," pp. 355-76 of Sungenis, Not By Bread Alone (2d ed.). On this, note the following from Dominican theologian Reginald Garrigou-Lagrange:
IS THERE SACRIFICE IN HEAVEN?
This has been
admitted by some and in recent times by Talhofer and Father Lepin because
Christ offers to God the Father His glorious scars and because the Scripture
says: “I saw the Lamb standing as it were slain” (Apoc. 5:6).
There is a
considerable difficulty here, because first of all sacrifice in the strict
sense implies external immolation, at least sacramentally, and this does not
continue in heaven any more than the sacraments do, because the blessed see God
directly, without sensible signs.
Moreover, it seems
that the sacrifice in heaven would not be subordinated, but coordinated with the
sacrifice on the cross, whereby therefore the work of our redemption would not
have been completed, and would be contrary to what our Lord said in dying: “It
is consummated” (John 19:30). In fact, it seems that the sacrifice in heaven as
such would be more perfect than the sacrifice on the cross, which latter would
be subordinated to it as a disposition to its ultimate perfection.
Wherefore neither a
new sacrifice in heaven in the strict sense must be admitted, nor a new and
formal oblation of the sacrifice on the cross, but merely its consummation,
which, St. Thomas says, “consists in this, that those for whom the sacrifice is
offered, obtain the end of the sacrifice . . . according to Heb. 9:11, that
Christ is a high priest of the good things to come, for which reason the priesthood
of Christ is said to be eternal” (Summa theol., IIIa, q. 22, a. 5, c).
Nevertheless, until
the end of the world, Christ glorious appeals to the Father for us, as the
fruits of the sacrifice on the cross are applied to us, and thus also He
actually offers the Masses that are daily offered by His priests. After the end
of the world, Christ as our High Priest along with the members of His mystical
body, will offer to the Father the cult of praise, adoration, and thanksgiving,
wherein the sacrifice on the cross will be consummated without a new sacrifice
in the strict sense (cf. Heb. 7:24 f.; 9:12 f., 24 f.; 10:12 f.; 1 Cor. 15:55
f.; Rom. 6:6 f.; Col. 2;14 f.).
The sacrifice of the
cross, however, is not actually but virtually perpetuated in its consummation;
for it is more perfect to reach consummation than to tend toward it, and the
mystical body already glorified is more perfect than the mystical body not yet
glorified. Likewise, generally speaking, merit is subordinated to the reward
toward which it tends. (Reginald Garrigou-Lagrange, Christ the Savior: A Commentary
on the Third Part of St. Thomas’ Theological Summa [trans. Dom Bede Rose;
London: B. Herder Book Company, 1950, 1957], 688-89)
