A Scripture verse to point your friend to is Colossians 1:24: “Now I [Paul] rejoice in my sufferings for your sake, and in my flesh I complete what is lacking in Christ’s afflictions for the sake of his body, that is, the church.”
Paul doesn’t mean that Christ’s death is insufficient for universal redemption. He is simply saying that his own incorporation into the mystical body of Christ (the Church) means that his sufferings can be helpful for other members of the body (the Colossian Christians to whom he is writing). They are helpful only because Paul is united to Christ in his Church and is offering his sufferings to Christ for the sake of the Church.
In the same way, suffering souls can similarly offer up their sufferings for the benefit of others.