The Greek text according to the NA28 states,
ΙΑʹ Τῇ δὲ ἐπιούσῃ νυκτὶ ἐπιστὰς αὐτῷ ὁ κύριος εἶπεν· θάρσει· ὡς γὰρ διεμαρτύρω τὰ περὶ ἐμοῦ εἰς Ἰερουσαλήμ, οὕτως σε δεῖ καὶ εἰς Ῥώμην μαρτυρῆσαι. NA28, ©2012
According to LSJ on the verb ἐφίστημι,1
III. stand by or near, ὣς πυκνοὶ ἐφέστασαν ἀλλήλοισιν Il.13.133; ἐπʼ ἄκρῳ χείλει ἐφεσταότες, ἐ. παρὰ τάφρῳ, 12.52, 199; θύρῃσιν ἐφίστατο 11.644; ἐπὶ τὰς πύλας, ἐπὶ τὰς θύρας, Hdt.3.77, Pl.Smp.212d; ἐπὶ τοῖς προθύροις Id.Phlb.64c; esp. of dreams or visions, appear to, εὕδοντι ἐπέστη ὄνειρος Hdt.1.34, cf. 7.14; ὄναρ κεφαλῆφιν ἐπέστη Il.10.496; ἐπιστᾶσα τῆς νυκτός Isoc.10.65; ἄγγελος ἐπέστη αὐτοῖς Ev.Luc.2.9: abs., stand by, Hdt.3.78; πολλῶν ἐφεστώτων App.Syr.10; ἤμην ἐφεστώς Act.Ap.22.20; οἱ λέβητες ἐπεστεῶτες Hdt.1.59; ὁ ἀντίδικος ἐφέστηκε Pl.Tht.172e, cf. Aeschin.3.79; without hostile sense, ἐπέστης S.OC558, cf. Ev.Luc.2.38, etc.; of troops, to be posted after or behind, κατόπιν ἐ. τοῖς θηρίοις Plb.16.18.7.
The reference in Isocrates2 has a strikingly similar phrase with that of Acts (written by Luke).
ἐπιστᾶσα τῆς νυκτὸς Ὁμήρῳ...
after she appeared to Homer at night...
We find ἐφίστημι again conjugated as an aorist participle (viz., ἐπιστᾶσα), the object of the verb again declined in the dative (viz., Ὁμήρῳ), with the scene occurring at night.
On Acts 23:11, Meyer comments,3
Whether the appearance of Christ encouraging Paul to further stedfastness was a vision in a dream, or a vision in a waking state, perhaps in an ecstasy, cannot be determined (in opposition to Olshausen, who holds the latter as decided, see on Acts 16:9).
Michael R. Licona likewise comments,4
In Acts 23:11, Jesus appeared to Paul at night. Did this occur in a dream? If it was an appearance in the same room as Paul, was it of the same nature as his conversion experience? The text does not say.
Can ἐφίστημι be understood in the context of a physical presence, as though the Lord Jesus Christ in his very person was standing by the apostle Paul? Certainly.
For example, in Iliad,5
fencing spear with spear, and shield with serried shield; buckler pressed on buckler, helm on helm, and man on man; and the horse-hair crests on the bright helmet-ridges touched each other, as the men moved their heads, in such close array stood they one by another, and spears in stout hands overlapped each other, as they were brandished,
φράξαντες δόρυ δουρί, σάκος σάκεϊ προθελύμνῳ: ἀσπὶς ἄρ᾽ ἀσπίδ᾽ ἔρειδε, κόρυς κόρυν, ἀνέρα δ᾽ ἀνήρ: ψαῦον δ᾽ ἱππόκομοι κόρυθες λαμπροῖσι φάλοισι νευόντων, ὡς πυκνοὶ ἐφέστασαν ἀλλήλοισιν
I don’t think I can provide any examples in the Greek NT of this occurring (“this” being: ἐφίστημι + dative of person) in the absence of supernatural entities.6 However, it is certainly attested elsewhere in classical Greek literature.
All that being said, I would opine that Acts 23:11 describes a vision occurring at night in which the Lord Jesus Christ appears to the apostle Paul. This is an allusion, like all the other visions and dreams in the Acts of the Apostles,7 to Joel’s prophecy:8
28 “And it shall come to pass afterward
That I will pour out My Spirit on all flesh;
Your sons and your daughters shall prophesy,
Your old men shall dream dreams,
Your young men shall see visions. NKJV, ©1982
Again, whether it was a vision in a dream, or a vision while awake, it does not seem as though the text provides ample info to determine that.
1 LSJ, p. 745
2 Helena (Ἑλένη), Book 10, §65. I borrow the verb “appeared” from Norlin’s translation (cited below).
3 Meyer, p. 431
4 Licona, p. 395
6 I think it would be important to exclude the presence of supernatural entities in the context since it would prove the meaning of “stand by” rather than “appear to.”
7 see Miller, John B. F. Convinced that God has Called Us: Dreams, Visions, and the Perception of God’s Will in Luke–Acts. Leiden: Brill, 2007 (p. 231). Unfortunately, Miller doesn’t offer much more substantial insight into Acts 23:11 than what has already been discussed.
8 Joel 2:28
Homer. Homeri Opera in Five Volumes. Oxford: Oxford UP, 1920.
Homer. The Iliad with an English Translation. Trans. Murray, Augustus Taber. Cambridge: Harvard UP, 1924.
Isocrates. Isocrates with an English Translation in Three Volumes. Trans. Norlin, George. Cambridge: Harvard UP, 1980.
Licona, Michael R. The Resurrection of Jesus: A New Historiographical Approach. Downers Grove: InterVarsity, 2010.
Liddell, Henry George; Scott, Robert; et al. A Greek-English Lexicon. 9th ed. Oxford: Clarendon, 1940.
Meyer, Heinrich August Wilhelm. Critical and Exegetical Handbook to the Acts of the Apostles. Trans. Gloag, Paton James. Ed. Dickson, William P. 2nd ed. New York: Funk, 1889.