How does uniting to Christ's suffering work?

Question

What is the Catholic teaching on uniting with Christ's suffering?

Specifically when we go through some kind of suffering and we acknowledge it as God's will and converse it with Christ. It reminds us of His suffering and helps us to realize what Christ did for us.

My question is: Does it also subtract from his suffering? When he went through his passion Jesus saw all sins of past, present, and future. But he also saw the fruit and the saint's responds which gave him comfort. Does uniting to Christ's suffering only comforts the heart of Jesus or also subtract his suffering during crucifixion where he would otherwise have gone through them?

For example: If I suffer some pain and take it as sharing Jesus's suffering, was that sharing now split between me and him and now Christ doesn't need to suffer as much(back in time) because I took some part on myself?

"In bringing about the Redemption through suffering, Christ raised human suffering to the level of the Redemption. Thus each man, in his sufferings, can also become a sharer in the redemptive suffering of Christ" (Salvifici Doloris).

Answer 1

In his commentary on St. Paul's letter to the Colossians, St. Thomas Aquinas says the following regarding v. 1:24 ("…fill[ing] up those things that are wanting of the sufferings of Christ, in my flesh, for his body, which is the church"):

61. – … At first glance these words can be misunderstood to mean that the passion of Christ was not sufficient for our redemption, and that the sufferings of the saints were added to complete it. But this is heretical, because the blood of Christ is sufficient to redeem many worlds: “He is the expiation for our sins, and not for ours only but also for the sins of the whole world” (1 Jn 2:2). Rather, we should understand that Christ and the Church are one mystical person, whose head is Christ, and whose body is all the just, for every just person is a member of this head: “individually members” (1 Cor. 12:27). Now God in his predestination has arranged how much merit will exist throughout the entire Church, both in the head and in the members, just as he has predestined the number of the elect. And among these merits, the sufferings of the holy martyrs occupy a prominent place. For while the merits of Christ, the head, are infinite, each saint displays some merits in a limited degree. This is why he says, I complete what is lacking in Christ’s afflictions, that is, what is lacking in the afflictions of the whole Church, of which Christ is the head. I complete, that is, I add my own amount; and I do this in my flesh, that is, it is I myself who am suffering. Or, we could say that Paul was completing the sufferings that were lacking in his own flesh; for what was lacking was that, just as Christ had suffered in his own body, so he should also suffer in Paul, his member, and in similar ways in others. And Paul does this for the sake of his body, which is the Church that was to be redeemed by Christ: “That he might present the Church to himself in splendor, without spot or wrinkle” (Eph 5:27). In the same way all the saints suffer for the Church, which receives strength from their example. The Gloss says that “afflictions are still lacking, because the treasure house of the Church’s merits is not full, and it will not be full until the end of the world.”

So, to answer your questions:

Does it also subtract from his suffering? … Does uniting to Christ's suffering … subtract his suffering during crucifixion where he would otherwise have gone through them?

No, there is no subtraction of His suffering. He could've redeemed us with one drop of his most precious Blood or even without suffering at all, but He chose* to suffer to the extent He did to pay our debt to sin superabundantly, to show His immense love for us.

^{*cf. Is. 53:7: "He was offered because it was his own will"}