Biblically there's is a phrase for the Spirit of God the Father and the Spirit of Christ the Son. And the Holy Spirit proceeds from the Father and the Son.
How about the "Spirit" of the Holy Spirit? Looking at it, it seems that, the thing called "spirit" do not point to the Three Person in the Triune God. The phrase would mean as if the Triune God has a "spirit" that animates the three person namely, Father Son and the Holy Spirit.
God is a Spirit, how come God who is a Spirit also has a "spirit"?
Comparing to a created man who is composed of body and soul. The soul animates the body and the spirit animates the soul.
Is God who existed in eternity as Spirit animated by "spirit" too?
What is the logical and biblical understanding of the "spirit" of the Father, Son and the Holy Spirit?
Catholicism is preferred but a Christian biblical understanding is also welcome.