The Trinity teaching is not biblical. Spiritual possession on the other hand is. One can be led by "the spirit" of demons or the spirit of the creator. Jesus was constantly accused by the adversary of man along with his minions of being possessed of demons but he retorted by saying that Satan cannot cast out Satan. Jesus was the first human being that while having faulty human DNA (if you will) was made perfect by the indwelling spirit of his father. Because he himself had no human father it was God himself who sired his paternal DNA. Jesus said that it was his father who was his guide. Unlike you and me, he like Adam had the blueprint for following God built right in and much like Adam was able to access it as a source for making the right choices.
Adam however fouled it up for himself and his offspring by cutting of this life link through willful disregard of its instruction, something that Jesus emphatically did not and unlike Adam, Jesus had a fouled up blueprint that he inherited from his mother's side that constantly opened him up to attacks from the adversary of man and to second guessing. This is what makes his sacrifice so great. Jesus devoted his life to selfless obedience for the sake of humanity. This is why God's gift is so great, because without the direct infusion of his spirit back into humanity (a second chance if you will) Jesus could not have lived a sinless life.
It is this cooperation between The Heavenly Father and his only begotten (that means sired) son that gets to be played out over and over again in the lives of believers throughout the ages. It is because he did not give in to his human nature but instead tenaciously followed his father's guidance that he was able to overcome the world and why we have hope now and are able to be grafted on as children of God.
There is no three headed God ruling the universe. God has only one head. He is only one. He has only one spirit and it is a living spirit (not a force or energy) that permeates every fiber of the cosmos and that animates all living things. The bible speaks of him and him alone as the source of life. If you seek a multi-headed god then you have to look in the book of Revelation because it is there that it describes a Dragon with seven heads that seeks to usurp the power of the almighty and that dragon is identified as the enemy himself Satan.