I think that God has many Spirits; yes, I think that is certainly possible. I don't understand it, but still God may have upwards of at least seven spirits, Rev. 4:5 describes seven spirits of God. What those spirits are, I just don't know; I mean I have some speculations, but I am not sure yet. I think one of those spirits is life itself; conscious life, or I think it fair to say just " Consciousness"; and I view the spirit of life, or consciousness, as being what the bible describes as " The Image of God." So when the bible states that we were created in the image of God, it means we are conscious beings, as God is a conscious being; and I think that's the ONLY thing we have in common with God, in my personal view; we are nothingelse like him!
So all humans ever created have that spirit IN them, consciousness. We were born with it. God blowing the breath of life into a human, means he gave their body consciousness.
Now, the " Holy Spirit of God", is another one of those seven, its FAR different than consciousness. That Spirit is a conversion new birth, which I think causes a lot more confusion with us who are learning. I think a human can have the down payment of that spirit actually IN them , while they are in the flesh, but it is never full blown until they are changed into a Spirit being, which is what being born again really means- a totally new birth! Now the human is an actual spirit being, unable to ever sin again! And I see that as being the predestined future of ALL humans!
So ALL humans have at least one spirit of God in them, life, and through this Christ is ALL and IN All! We are predestined to receive a second Spirit, the Holy Spirit, when we are changed; but that Spirit can be "with" some now!