Fr. Reginald Garrigou‑Lagrange, O.P. discusses the office of mediator:
"The office of mediator belongs fully only to Jesus, the Man‑God, Who alone could reconcile us with God by offering Him, on behalf of men, the infinite sacrifice of the Cross, which is perpetuated in Holy Mass. He alone, as Head of mankind, could merit for us in justice the grace of salvation and apply it to those who do not reject His saving action. It is as man that He is mediator, but as a Man in Whom humanity is united hypostatically to the Word and endowed with the fullness of grace, the grace of Headship, which overflows on men. As St. Paul puts it: 'For there is one God, and one mediator of God and men, the man Christ Jesus: Who gave Himself for a redemption for all, a testimony in due times' (I Tim. ii, 56). "But, St. Thomas adds: 'there is no reason why there should not be, after Christ, other secondary mediators between God and men, who co‑operate in uniting them in a ministerial and dispositive manner.’ Such mediators dispose men for the action of the principal Mediator, or transmit it, but always in dependence on His merits.” [1]
Actually there is a reason, God made no provision for other mediators His word. In Fact He clearly excludes another
1 Tim2:5 For there is one God, and one mediator of God and men, the man Christ Jesus: 6 Who gave himself a redemption for all, a testimony in due times
"St Thomas'" words were not added to the infallible scriptures they are his own personal opinion and nothing more
Then Christians shouldn't pray for each other, because that's mediation.
His word. In Fact He clearly excludes another
In fact, 1 Tim 2:5 does nothing of the sort, and says nothing like what you claim it says. The word translated "one" is heis ("one, unique, primary"), not monos ("one and only one").
But you don't even need to know Greek to see that. Read it in context:
1 Therefore I exhort first of all that supplications, prayers, intercessions, and giving of thanks be made for all men, 2 for kings and all who are in authority, that we may lead a quiet and peaceable life in all godliness and reverence.
If you look up "intercession" in the dictionary, you'll find that it's mediation for a lesser party before a greater party. All you have to do is look two verses away to see that your exegesis is wrong.
Paul's point here is not that Christians mediate before the Father in place of Christ -- and no Christian believes that they do -- but the Christians are commanded to mediate for each other with Christ, not instead of him, and he -- the one mediator -- then mediates those petitions to the Father.
Mary doesn't mediate with the Father except through and in Christ, Paul doesn't, Timothy doesn't, the Pope doesn't, I don't, and you don't. That's Catholic doctrine, and it's Biblical doctrine.
As I've said before, Protestants only believe in this "only one mediator" stuff when they use it to attack Catholicism. The rest of the time, they're busy publishing "prayer requests" which ought to be totally out of line if there's only one mediator.