There actually had been attempts to do this. For example:

There was an early Christian "heresy" called Arianism, which formed during the time of Constantine the Great by a bishop named Arius. They believed that Christ as divine, but had a lesser divinity than God the Father. This didn't sit well with the Church leaders who believed firmly in the Trinity (I.E. there is God the Father, God the Son, and God the Holy Spirit, equal in power forming God but each being distinct from the other), prompting the first ecumenical council to decided if Arius' teaching was heresy. Considering I described Arianism as an early heresy, it should be easy to tell that the council did not vote in Arius' favor.

Fun Fact: It was recorded that Saint Nick, yes, the bishop who partially inspired Santa Claus, punched Arius in the face.

Anyway... Muhammad stated that Jesus was another one of God's prophets. An important prophet to be sure, but, like Muhammad himself, Jesus is not divine. As you said, Islam hammers down the point that there is one, single, GOD.

Over a thousand years after Muhammad's time, Thomas Jefferson (yes, the one who wrote the US' declaration of Independence) also rewrote the Bible in his spare time to eliminate all the "supernatural" parts that clashed with "Enlightenment" mindset.