I believe it’s God’s Spirit which gives Him His glory. Called “the Spirit of the LORD” or “the Spirit of God” .
For example, He created the heavens and earth by His Spirit. And He performed all sorts of miracles by His Spirit. The Scripture was ultimately written by His Spirit.
God could give a measure of His Spirit without diminishing His Spirit.
God can also give a full measure of His Spirit without diminishing His own.
God gives a full measure of His Spirit to His son only. In that way the son would share in the same glory as God.
Rom 8:9 You, however, are not in the flesh but in the Spirit, if in fact
the Spirit of God dwells in you. Anyone who does not have
the Spirit of Christ does not belong to him.
Rom 8:10 But
if Christ is in you, although the body is dead because of sin, the Spirit is life because of righteousness.
Rom 8:11 If
the Spirit of him who raised Jesus from the dead dwells in you, he who raised Christ Jesus from the dead will also give life to your mortal bodies through his Spirit who dwells in you.
Rom 8:12 So then, brothers, we are debtors, not to the flesh, to live according to the flesh.
Rom 8:13 For if you live according to the flesh you will die, but if by the Spirit you put to death the deeds of the body, you will live.
Rom 8:14 For all who are led by
the Spirit of God are sons of God.
Rom 8:15 For you did not receive the spirit of slavery to fall back into fear, but you have received
the Spirit of adoption as sons, by whom we cry, "Abba! Father!"
Rom 8:16 The Spirit himself bears witness with our spirit that we are children of God, (ESV)
Compare that with what Paul says in
Galatians 4:
Gal 4:6 And because you are sons, God has sent
the Spirit of his Son into our hearts, crying, "Abba! Father!" (ESV)
Php 1:19 for I know that through your prayers and the help of
the Spirit of Jesus Christ this will turn out for my deliverance, (ESV)
And, very importantly, in 1 Peter we see that the OT prophets prophesied by the "Spirit of Christ":
1Pe 1:10 Concerning this salvation, the prophets who prophesied about the grace that was to be yours searched and inquired carefully,
1Pe 1:11 inquiring what person or time
the Spirit of Christ in them was indicating when he predicted the sufferings of Christ and the subsequent glories. (ESV)
There are two very significant things going on in those passages. First, the Holy Spirit is not only called the Spirit of God, he is also called the Spirit of Christ and the Spirit of his Son. Second, Peter clearly states that it was by the Spirit of Christ that the OT prophets prophesied about Christ.