Christ said to "do this in memory of Me."
Not "do this pretending to be Me."
Therefore no one "acts in the person of Christ." No one is "another Christ." There is only one Savior, King and Redeemer, Jesus Christ, and his substitutionary atonement for His sheep is complete. God has accepted Christ's sacrifice, attributing His righteousness to our account and His death as satisfaction for our sins. Therefore our sins have been forgiven and there is no more offering for sin.
From henceforth expecting till his enemies be made his footstool. For by one offering he hath perfected for ever them that are sanctified. Whereof the Holy Ghost also is a witness to us: for after that he had said before, This is the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them; And their sins and iniquities will I remember no more. Now where remission of these is, there is no more offering for sin." -- Hebrews 10:12-18"But this man, after he had offered one sacrifice for sins for ever, sat down on the right hand of God;
There is no pretense: Christ also said, “I send you like my Father send me” and “whoever hears you hears me”. That relationship of sacramental agency is what “alter Christus” so economically signifies.
Every Mass is that singular offering at Golgotha, rather than a separate offering, just like Hebrews 10 teaches.