Usage: 2 forms in 2 verses
Form Translated As     In Verse(s)
προσγενόμενοσ uniting LXX.Lev.18.26
προσγένηται should unite LXX.Num.15.14

Liddell-Scott-Jones

προσγίνομαι (prosginomai) unite with G:V

προσγίνομαι,

Ionic dialect and later προσγίν- [], attach oneself to another, especially as an ally, τινι [Refs 5th c.BC+]; θαρσεῖν τοῖς προσγιγνομένοις by the reinforcements, [Refs 5th c.BC+]; also in political strife, προσγενομένου τοῦ δήμου αὐτῷ [Refs 5th c.BC+]

__2 generally, to be added, accrue, [Refs 5th c.BC+]; ἐκ τῶν σιτίων ταῖς σαρξὶ σάρκες π. [Refs 5th c.BC+]; opposed to ἀπογίγνομαι, χωρίζομαι, [Refs 5th c.BC+]
__3 come to, happen to, τοῖς γὰρ θανοῦσι μόχθος οὐ π. [Refs 5th c.BC+]
__4 become in addition, πρὸς τῷ θυμοειδεῖ ἔτι π. φιλόσοφος [Refs]