ὁ δὲ κολλώμενος τῷ Κυρίῳ ἓν πνεῦμά ἐστιν.
"But anyone united to the Lord becomes one spirit with him" (NRSVue).
Paul argues that Christians should cleave to Jesus and his way of life, remembering his grace and faithfulness. Then, a Christian's spirit will be united with the spirit of Christ, which means there is one mind, one will, and one action that seeks God's will on earth: all people's deliverance from evil and their sanctification.
Otherwise, Paul does not seek a mere unity of the community like the hierarchical conception of a society based on homonoia (unity or concord) that does not advocate for the weak members. Rather, he envisions a new community of God based on Christly examples. This vision will be realized only when people share in the spirit of Jesus, following his way of life.
Likewise, in 1 Cor 12:27 ("You are the body of Christ, and individually members of it"), his argument is not to establish a unified community based on an organism model but to emphasize Christ-ruled living and community. That is, Christ-followers must embody his spirit. The Corinthians are a Christic body, a Christ-ruled community. Individually and communally, they must follow the way of Jesus. The sense of the body Paul uses here is not an organism but a site of living (cf, 1 Cor 6:20: "For you were bought with a price; therefore, glorify God in your body").
For more about this argument, you may want to read my recent book How to Read Paul: A Brief Introduction to His Theology, Writings, and World and other articles, including “Reclaiming Christ’s Body (soma christou): Embodiment of God’s Gospel in Paul’s Letters,” Interpretation 67.1 (2013): 20-29.
The above point began with my doctoral dissertation, which led to the publication of my debut book, Christ's Body in Corinth: The Politics of a Metaphor, in 2008.