Question on the Trinity

[Thy Geekdom Come]

We know that the love of the Trinity means that the Father and Son give Themselves each over to the Other, but does the Holy Spirit give Himself over as well? We are taught in the Athanasian Creed that the Father and Son are Generator and Generated, but that the Holy Spirit proceeds. It would appear than that while the Father and the Son give Themselves over to one another, the Holy Spirit does not take His Being and give it to the others, but only "transmits" (closest word I can seem to find to define the action) the Being of the Triune God between Father and Son.

Perhaps when the Father gives His Being to the Son and the Son to the Father through the Holy Spirit, Each gives the Being to the Holy Spirit, Who in turn gives it to the Others, thus allowing Each Person of the Holy Trinity to give and receive on His own account. Is this plausible?

I would find it odd that the Holy Spirit did not give over Himself, being all loving, but I want to make sure I have the orthodox position.

[Laudate_Dominum]

The Holy Trinity is Perfect Gift.

The Father is unoriginate self-diffusive Goodness and is neither begotten nor spirated. The total expression of the Father is the Son, Who is begotten. The Son also participates in the generation of the Spirit who's mode in this schema of logical distinctions is passive (in an analogous sense).
I'm trying to use non-technical language so this lacks precision, forgive me.
So the character of the Person's gift can be describes in these terms:
Father - Originates
Son - Receptive and Originating
Spirit - Receptive

When discussing persons receptivity is not the same as pure passivity, because the will (the whole person really) is active in sanctioning and participating the whatever it is.

This is a radical simplification and I'm weary of posting it because people might misunderstand or derive false conclusions..

On a side note, the fact of the Word's receptive and originating role can be elucidated in such a way that it becomes evident why, among the Persons of the Trinity, it was fitting that the Word became Incarnate.

To really answer your question I'd have to post a hefty volume.