It seems to me that Paul’s epistle to Philemon is structured chiastically:
A Greetings and Grace (1-3)
B Paul’s Prayers (4)
C Partnership & Refreshed Hearts (5-7)
D Appeal for Onesimus (8-11)
E Sending Onesimus back to be “Paul” to Philemon (12)
E’ Wishing to Keep Onesimus to be “Philemon” to Paul (13)
D’ Appeal for Onesimus (14-16)
C’ Partnership & Refreshed Hearts (17-21)
B’ Paul Granted through Philemonâ€™s Prayers (22)
A’ Greetings and Grace (23-25)
In A and A’, there are the fairly typical greetings culminating in a blessing.
In B, we have Paul making memorial of Philemon in his prayers. In B’, Paul tells Philemon to prepare a guest room for him because he trusts that he will be granted to Philemon through Philemon’s prayers. So Paul is memorializing Philemon (B), and Philemon is memorializing Paul (B’) before the Lord.
In C, Paul talks about Philemon’s “partnership” (koinonia) and about his joy because because Philemon has refreshed the hearts of the saints. In C’, Paul says that if Philemon regards him as a “partner” (koinonos), he should refresh his heart.
In D, Paul begins his appeal for “my son Onesimus” who was once unprofitable but now is profitable to Paul and to Philemon. He doesn’t want to command but to appeal. In D’, Paul says that he didn’t want to act without Philemon’s consent but rather wants Philemon to act voluntarily, which relates to the earlier statement about appealing instead of commanding. He speaks here of Philemon receiving Onesimus as “more than a slave,” which relates to Onesimus’s usefulness. He is a “brother” to Philemon and Paul, linking up with the family language (“son”) in D.
It seems to me that the hinge of the whole letter is E and E’, where Paul says that he is sending Onesimus back for Philemon to receive, and when he receives him, Philemon will be receiving Paul. But he wishes to keep Onesimus to represent Philemon to Paul, ministering to him “on your behalf.” Onesimus is thus the bearer of Paul’s identity to Philemon and of Philemon’s to Paul.