This doctrine, `For you and for many' is fascinatingly explained in the book, "The Mystical City of God, The Transfixion, Part II" in the prayer Our Lord made while in the Garden of Gethsemane:
Ven. Mary of Jesusof Agreda (1602 - 1665):
501 He prostrated Himself with His Divine face upon the ground and prayed to the eternal Father:
My Father, if it be possible, let this chalice pass from Me.
502 "... I must state that on this occasion Jesus our Redeemer conferred with the eternal Father about the arduous affair between them, namely how human Redemption and the fruit of His Passion and Death of the cross would affect the predestination of the saints. In this prayer, Christ offered on his part to the eternal Father his torments, his precious blood, and his death for all men as an abundant price for all mortals and for each one of the human race. He presented the sins, infidelities, ingratitude and contempt which the wicked for whom He suffered, were to commit in wasting his frightful Passion and Death, the effect of which would be their condemnation to eternal punishment for not having availed themselves of his clemency.
Though to die for his friends and for the predestined was agreeable as if were appealing to our Savior, yet to suffer and die for the reprobate was very bitter and painful, for regarding them the ultimate reason for suffering and death was lacking.
503 Therefore I understood that in this prayer Christ our Lord besought his Father to let this most
bitter chalice of dying for the reprobate pass from Him. Since now his death was inevitable He asked that no one, if possible, would be lost. He pleaded that as his Redemption would be superabundant for all it thus be applied to all in such a way as to make all, if possible profit by it in an efficacious manner, yet if this was not possible, He would resign Himself to the will of his eternal Father. Our Savior repeated this prayer three times at different intervals (Mt. 26:24), pleading the longer in his agony (Lk. 22:43) due to the importance and immensity of the object in question.
According to our way of understanding, in this meditation there was as it were a contention or altercation between the most holy humanity of Christ and the Divinity; for the humanity, with personal love for men who were of his own nature, desired all to attain eternal salvation through his Passion, while the Divinity represented that by his most exalted judgements and the number of the predestined was fixed, and in accordance with the equity of justice He could not concede this benefit. to those who despised it so much, and who of their own free will made themselves unworthy of the Life of souls, resisting Him who procured and offered it to them. From this conflict resulted the agony of Christ and his prolonged prayer, pleading the power of his eternal Father, and that all things were possible to his infinite majesty and grandeur (Mk. 14:36).
504 This agony of Christ our Savior grew in proportion to the greatness of his charity and the certainty of his knowledge that men would persist in neglecting to profit by his Passion and Death. His agony increased to such an extent that great drops of bloody sweat were pressed from Him which flowed to the very earth (Lk. 22:44). Although this prayer was uttered subject to a condition and failed in regard to the reprobate who fell under this condition, yet He gained by it greater and more frequent helps for all mortals, and their multiplication for those who would accept them and place no obstacle to them.
Through his prayer the just and the saints would participate in the fruit of the Redemption with greater abundance and many gifts and graces of which the reprobate made themselves unworthy were applied to the elect. The human will of Christ, conforming itself to the divine will, then accepted the Passion for each one respectively: for the reprobate as sufficient, since they would be given sufficient helps if they desired to avail themselves of them, and for the predestined as efficacious, since they would cooperate with grace.
Thus was set in order and as it were realized the salvation of the Mystical Body of the holy Church, under its Head and Architect, Christ our Good (Col. 1:18).