There is an entire doctrine built around this concept. I believe Wesley formulated it. It is called Entire Sanctification. (Wesley, IIRC, never claimed to have reached this state.)
The doctrine of sanctification runs through the NT. Romans 12:2 say we are to be transformed by the renewing of our minds. Entire Sanctification would be the completion of this process that perhaps is only theoretically possible.
In any case, if Spirit is fundamentally other (other than physical reality) and that Spirit that we have is, say, on loan from God. Then perhaps the prayer to be more like God isn't so far out of line.
When I was an elder I some times taught like this: When we become saved we are adopted into the family of God (adoption language runs through Paul's letters). As we are sanctified, that is to say, transformed, the miracle of salvation is our transformation into the "Blood" children of God. This isn't to say that if you die "early", you won't get to go to heaven. This is just a metaphor about what the process is about.
But all of the above is more mystical than necessary. To be like God can be simply interpreted as being more loving, more just, more merciful, more patient, more all-of-the-fruit-of-the-spirit.
So, in either case, a justification can be made to pray "Let me be more like you." In the first case, you are praying that God "continue that work which was begun in you." The second case is like the first, but without the mystical overtones.