Christopher Porter has produced individual treatments of each of the Letters to Timothy and Titus from a social identity perspective:
Porter, Christopher A. “1 Timothy.” Pages 445–60 in T&T Clark Social Identity Commentary on the New Testament. Edited by J. Brian Tucker and Aaron Kuecker. Edinburgh: T&T Clark, 2020.
________. “2 Timothy.” Pages 461–68 in T&T Clark Social Identity Commentary on the New Testament. Edited by J. Brian Tucker and Aaron Kuecker. Edinburgh: T&T Clark, 2020.
________. “Titus.” Pages 469–73 in T&T Clark Social Identity Commentary on the New Testament. Edited by J. Brian Tucker and Aaron Kuecker. Edinburgh: T&T Clark, 2020.
Porter makes the front matter for the volume available on his Academia page.