Nate,
Smyth and Cooper appear to disagree.
Smyth 2001b
ἄν (κέ) does not appreciably affect the meaning.
Cooper 1:54.8.4 p. 717, observes that we never see ἄν with ἵνα because ἵνα is unambiguously final: in order that at, whereas ὅπως ἂν with subjunctive means something like: to see if. Just to see if Cooper was right I searched for ἵνα ἄν with subjunctive. It appears in
Aristoteles et Corpus Aristotelicum Phil., Ἀθηναίων πολιτεία
Section 55, subsection 4, line 8
νῦν δ᾽ ἀνάγκη πάντας ἐστὶ διαψηφίζεσθαι περὶ αὐτῶν, ἵνα ἄν τις πονηρὸς ὢν ἀπαλλάξῃ τοὺς κατηγόρους, ἐπὶ τοῖς δικασταῖς γένηται τοῦτον ἀποδοκιμάσαι.
but now all are compelled to vote one way or the other about them, in order that if anyone being a rascal has got rid of his accusers,1 it may rest with the jurymen to disqualify him.
Trans. H. Rackham.
Hippocrates et Corpus Hippocraticum Med., De articulis (0627: 010)
“Oeuvres complètes d’Hippocrate, vol. 4”, Ed. Littré, É.
Paris: Baillière, 1844, Repr. 1962.
Section 11, line 50
Ἔκτοσθεν δὲ τῆς μασχάλης, δισσὰ μόνα ἐστὶ χωρία, ἵνα ἄν τις
ἐσχάρας θείη, τιμωρεούσας τῷ παθήματι· μίαν μὲν ἐν τῷ ἔμπρο-
σθεν μεσηγὺ τῆς τε κεφαλῆς τοῦ βραχίονος καὶ τοῦ τένοντος τοῦ
κατὰ τὴν μασχάλην·
Hippocrates et Corpus Hippocraticum Med., De semine, de natura pueri, de morbis iv
Section 51, line 20
Τούτων δ’ ἐόντων, ὅ τι ἂν ἐν νούσῳ
51.20
πλεῖστον ᾖ, ἐν ἀρχῇσι γινομένης τῆς ταραχῆς, ἔρχεται ἐς χωρίον
51.21
ἵνα ἂν πλεῖστον ἔῃ· ἐν δὲ τῇ ταραχῇ εὐρυχωρίης γινομένης, εἰ-
λέεται ἀποκεκριμένον καὶ θερμαίνει τὸ σῶμα
It also appears in Philo and Josephus but that is Koine and according to Margaret Sim[1] ἵνα in Koine is a whole different ball game.
[1]SIM, Margaret G., 2006. A relevance theoretic approach to the particle ἵνα in Koine Greek.