Even a Pharisee can come to believe in the Lord, some did so, as the scriptures testify. Saint Paul is one example that comes to mind. He said of himself
But when Paul perceived that the one part were Sadducees, and the other Pharisees, he cried out in the council, Men and brethren, I am a Pharisee, the son of a Pharisee: of the hope and resurrection of the dead I am called in question.
Acts 23:6
Thus it is not all pharisees who are not "my sheep", which I think you acknowledge, and it is possible that some among those addressed in John chapter ten became followers of the Lord.
And many believed on him there.
John 10:42
Read the chapter with care and observe that the sheepfold is not intended to exclude any except thieves and robbers, these were those who came before Christ arrived.
Then said Jesus unto them again, Verily, verily, I say unto you, I am the door of the sheep. All that ever came before me are thieves and robbers: but the sheep did not hear them.
John 10:7-8
Yet he says that
I am the door: by me if any man enter in, he shall be saved, and shall go in and out, and find pasture.
John 10:9
The door is the means by which any man may enter the sheepfold.
Some among the Jews objected and some listened.
There was a division therefore again among the Jews for these sayings. And many of them said, He hath a devil, and is mad; why hear ye him? Others said, These are not the words of him that hath a devil. Can a devil open the eyes of the blind?
John 10:19-21
And here is the passage to which you appeal so much yet misread, because it does not say Pharisees but Jews.
And it was at Jerusalem the feast of the dedication, and it was winter. And Jesus walked in the temple in Solomon's porch. Then came the Jews round about him, and said unto him, How long dost thou make us to doubt? If thou be the Christ, tell us plainly. Jesus answered them, I told you, and ye believed not: the works that I do in my Father's name, they bear witness of me. But ye believe not, because ye are not of my sheep, as I said unto you. My sheep hear my voice, and I know them, and they follow me: And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand.
John 10:22-28
You read "Pharisees" into your lesson because that suits your doctrine better than the words in the passage which are "the jews". But if you change to saying, "Scripture limits the atonement to many and denies its application to the Jews in Jesus' audience.", you would show yourself to be contradicting the scriptures shown above, specifically, John 10:19-21 and later in John 10:42.