You've probably heard this repeadedly and could have written it yourself (at least what is true, in this) but some things bear repeating, eh?
So, thanks for asking: yes, and more. (More constituent aspects of self exist of course, though as our FRiend - who is it now? I think we lost him - says, it all may come in three categories for all I know and as, I'm told, the reasonable old Greek whose name begins with a "P" also thought. It may seem that soul is kind of interstitial twixt spirit and body/physical, like a seemingly* big set of "drivers" and "interfaces." And then there's will. Shucks, thinking one way then another, it seems that all bits and pieces of us are laced with will, whether conscious or not.)
But really, more than the above and its "more," what is most about us is to see that how we are as beings is determined by why we are, as relaters. And so, the most fundamental aspect of me is not that I think, because being a being has an even more material purpose (and the same as the purpose for how I feel**). I am a relational being. Beyond this, I think it is even more fundamental to say, "I am a being of relationality." Function is an identifier, but purpose is a greater identifier, of both the function and the particular. And if we have a most important purpose, the functions of that purpose identify us more than any other functions we have.
Without resorting to Scriptures directly this time, I'll refer to what Henry Blackaby says (over and over and over again ;-) that our "calling" as he puts it, is to be in a deeply intimate loving relationship with God -- even a communion with Him! That's "the life that is truly life." (Oops, there's the Scripture.)
bb has just related that the ancient Greeks thought that Time is the image of Eternity. We are taught of course that we are created in the image of God. Images are stamped for purposes and the image that we who know God collectively have is that of God's very life mate for the person of his revelation to us. (How many folks in the Bible got queasy when they were given revelations? When you consider this, do you get butterflies? I just did. And more.)
This is our great, collective relationship and identity, yet it is made up of us each having an autonomous communion, God only and directly to and with the individual. In this way, as is Christ, so are we, his sons in Christ, and that is our individual identity. That most massive (or as the old Hebrews would say, "glorious") collective relationship is comprised of all these also infinite, autonomous relationships. So who am I? "I AM THAT I AM" has told me that I am a being of individual and collective communality with Him, autonomously imparted and maintained, and constituent in the collective "meet" of the revealed God. For this purpose, I am an individual of communal relationship: in God, therefore in my being, with all of the other adherents/constituents of the life partner of Christ, and in relational harmony to God with all else of His perfection. But for the time being, this is deeply encapsulated if you will in each of us. Presently, we may each have that autonomous sonship, plus have a kind of subdued communion in the invisible bride, not of this world, who is still 'putting herself together' in her dressing room.
And while bb's world is an open book from God, it also includes much hideous graffiti, but that's another part of the story. (And the most important player in the story by more than far, is God.)
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* probable partial credit to tortoise for "seemingly"
** Feelings, heart, soul, emotions... why do philosophers choose to ignore this so much in favor of reason? That is not just unreasonable but -- you know what? IT IRKS ME!
BTW, I'm still just a little queasy. How about you?
(Please forgive my imperfections, even though I have edited and "proof" read it quite a bit.)