Grammatically, there’s no reason for the verbal duplication. Thus, there appears to be an emotional or sentimental basis for it. Some interpret the passage as implying a disagreement between Euodias and Syntyche.
Theodoret of Cyrus wrote,2
On the one hand, [Paul] is amazed at the women, but on the other hand, he intimates them having a certain quarrel with one another.
θαυμάζει μὲν τὰς γυναῖκας· αἰνίττεται δὲ ὡς ἔριν τινὰ πρὸς ἀλλήλας ἐχούσας
Imagine, then, the apostle Paul appealing to both individually to settle their quarrel for the sake of Christian unity. Bengel wrote, “He puts this twice as though exhorting them apart personally, and that with the utmost equality.”2
1 p. 585
2 p. 730: “Hoc bis ponit, quasi coram adhortans seorsum utramvis, idque summa cum æquitate.”
Bengel, Johann Albrecht. Gnomon Novi Testamenti. Ed. Bengel, M. Ernest; Steudel, Johann, Heinrich. 3rd ed. London: Nutt, 1862.
Theodoret of Cyrus (Θεοδώρητος Κύρρου). “ΕΡΜΗΝΕΙΑ ΤΗΣ ΠΡΟΣ ΦΙΛΙΠΠΗΣΙΟΥΣ ΕΠΙΣΤΟΛΗΣ.” Patrologiæ Cursus Completus: Series Græca Prior. Ed. Migne, Jacques Paul. Vol. 82. Petit-Montrouge: Imprimerie Catholique, 1864.