I am not sure if there is anything in the definition that is technically incorrect, but I think the definition is misleading in that it suggests that cooperation is the essence of Semi-Pelagianism (I assume that this is the reason why you came to the conclusion that synergism and Semi-Pelagianism are one and the same, but please correct me if I am wrong).
I do not think that there are many modern Christians at all who believe in "grace plus something." Exactly who or what theology do you have in mind?
Catholics, for example, believe in the necessity of baptism and subsequent cooperation, but neither of these deny grace If you look at the canons of the council of orange, you will note that the council concluded the same:
Historic Church Documents at Reformed.org
CANON 5. If anyone says that not only the increase of faith but also its beginning and the very desire for faith, by which we believe in Him who justifies the ungodly and comes to the regeneration of holy
baptism -- if anyone says that this belongs to us by nature and not by a gift of grace, that is, by the inspiration of the Holy Spirit amending our will and turning it from unbelief to faith and from godlessness to godliness, it is proof that he is opposed to the teaching of the Apostles, for blessed Paul says, "And I am sure that he who began a good work in you will bring it to completion at the day of Jesus Christ" (
Phil. 1:6). And again, "For by grace you have been saved through faith; and this is not your own doing, it is the gift of God" (
Eph. 2:8). For those who state that the faith by which we believe in God is natural make all who are separated from the Church of Christ by definition in some measure believers.
. . .
CANON 8. If anyone maintains that some are able to come to the grace of
baptism by mercy but others through free will, which has manifestly been corrupted in all those who have been born after the transgression of the first man, it is proof that he has no place in the true faith. For he denies that the free will of all men has been weakened through the sin of the first man, or at least holds that it has been affected in such a way that they have still the ability to seek the mystery of eternal salvation by themselves without the revelation of God. The Lord himself shows how contradictory this is by declaring that no one is able to come to him "unless the Father who sent me draws him" (
John 6:44), as he also says to Peter, "Blessed are you, Simon Bar-Jona! For flesh and blood has not revealed this to you, but my Father who is in heaven" (
Matt. 16:17), and as the Apostle says, "No one can say 'Jesus is Lord' except by the Holy Spirit" (
1 Cor. 12:3).
. . .
CANON 13. Concerning the restoration of free will.
The freedom of will that was destroyed in the first man can be restored only by the grace of baptism, for what is lost can be returned only by the one who was able to give it. Hence the Truth itself declares: "So if the Son makes you free, you will be free indeed" (
John 8:36).
. . .
According to the catholic faith we also believe that after grace has been received through baptism, all baptized persons have the ability and responsibility, if they desire to labor faithfully, to perform with the aid and cooperation of Christ what is of essential importance in regard to the salvation of their soul. We not only do not believe that any are foreordained to evil by the power of God, but even state with utter abhorrence that if there are those who want to believe so evil a thing, they are anathema. We also believe and confess to our benefit that in every good work it is not we who take the initiative and are then assisted through the mercy of God, but God himself first inspires in us both faith in him and love for him without any previous good works of our own that deserve reward, so that we may both faithfully seek the sacrament of baptism, and after baptism be able by his help to do what is pleasing to him. We must therefore most evidently believe that the praiseworthy faith of the thief whom the Lord called to his home in paradise, and of Cornelius the centurion, to whom the angel of the Lord was sent, and of Zacchaeus, who was worthy to receive the Lord himself, was not a natural endowment but a gift of God's kindness.
If your point is that God must move towards man first (God giving man clothes, for example) then I would agree. From what I recall, the point I was attempting to make was that God's grace can be rejected (refusing to wear the clothes, or taking off the clothes, following the same analogy).