The Old Testament people of God believed that the sins of the dead could be atoned for by the living. 2 Maccabees 12:39-46 describes how Judas Maccabeus discovered that some of the men who had fallen in battle while fighting for their fellow Jews, were carrying amulets of the idols of Jamnia, which the law forbids the Jews to wear (v. 40).
Judas, reasoning that they had died as a punishment for sin, therefore “turned to prayer beseeching that the sin which had been committed might be wholly blotted out . . . He also took up a collection . . . and sent it to Jerusalem to provide for a sin offering. In doing this he acted very well and honorably . . . Therefore he made atonement for the dead, that they might be delivered from their sin” (42-43, 46).
Although a minority of Christians do not accept Maccabees as Scripture, disputing its canonicity does not negate its historical value. It shows that pious Jews believed in praying and making atonement for the dead shortly before the time of Jesus and the apostles.
It's this Jewish belief that Jesus was addressing when he said "... he shall suffer loss: but he himself shall be saved; yet so as by fire." (1 Corinthians 3:15) and "Thou shalt by no means come out thence, till thou hast paid the uttermost farthing." (Matthew 5:26).
He could not have meant Heaven, because he was speaking of a place of punishment. He can not have been speaking of Hell, because Hell is eternal: you never get out. He was speaking of a place or temporary state of being where you are released when you have "paid the last farthing."
The "Communion of Saints" means that we share spiritual goods with each other, both in this life and in the life to come. We pray for those who have passed on and pay these "last farthings" because we are the Body of Christ and He associates us in His saving work of love.
No one can fully atone of their own sins. It is Christ who gives this grace to us and through us, through our prayers for each other.
That's why Paul says, "First of all, then, I urge that petitions, prayers, intercessions, and thanksgiving be offered on behalf of all men" (1 Timothy 2:1)
What ability do you have to pay for your own sins or those of another?
That pretty much takes Christ out of your picture which means you are preaching another gospel.