Luke 23:23

The construction αἰτοῦσιν αὐτὸν σταυρωθῆναι should be understood as “they ask him to be staked/crucified”, with αὐτόν functioning as the person addressed (accusative of the person asked), and σταυρωθῆναι as the infinitive expressing the requested action.

This is a standard idiom in Greek: αἰτέω τινά τι ποιῆσαι, “to ask someone to do something.” It must be distinguished from “they ask for him to be crucified,” which would require a different construction—e.g., αἰτοῦσιν τὴν σταύρωσιν αὐτοῦ (“they ask for his crucifixion”) or αἰτοῦσιν ἵνα σταυρωθῇ (“they ask that he be crucified”). In the participial form, αἰτούμενοι αὐτὸν expects an infinitive complement to complete its sense.

Any time a pronoun follows this verb in the NT (him, father, me, etc.) it is refering to the person asked, not as an indirect object asked for.