Recent questions have arisen about the nature of the original NT texts and what counts as Koine Greek. To be honest, I have not devoted much time to this question in some time. But I've found old dialogues that might be helpful or that possibly show my progression of thought regarding the question. Here is one of those old discussions:
You have asked for a definition of Koine. As I mentioned, I do not feel comfortable defining it, but would much rather describe it. A number of phenomena are akin to Koine, in this respect. Try to define "justice" or "beauty" in a non-circular way that attracts nearly universal consensus and see what happens. I submit that we face the same challenge when we try to define Koine Greek.
First, however, I will say that Greek was definitely undergoing a change from Attic to "Koine" prior to Alexander's attempt to Hellenize non-Greek peoples and impose a Weltsprache on them. History shows that from the fourth century BCE-fourth century CE, a type of Greek was introduced which differed from the Greek found in Plato, Aristotle, Isocrates or even in Xenophon. Yet, this developing form of Greek was used in different media, like any other language. Thus, one finds a higher register of Koine in Josephus, Philo and Epictetus than might be found in the Greek papyri; but the dialect is the same. It is still Koine Greek, identified by its syntax, morphology, phonology, and idiomatic use. Whatever one may think concerning the grammatical features of what I am calling Koine Greek, it seems hard to dispute Alexander's influence on Greek and how it began to change as Alexander and his successors sought to bring about a common Weltsprache.
At any rate, I offer two examples for starters to show the nature of Koine Greek. My initial examples will come from Colwell's work The Greek of the Fourth Gospel.
Some (e.g., Burney, et al) who believe that John was originally writen in Aramaic think that the construction classified as CASUS PENDENS evidently found in 27 Johannine passages (Jn 1:12; 1:18; 3:26, etc) is a "Semitic" construction (See Colwell, 37). However, the construction is found in Classical Greek (cf. Xen. Cyr II.3.5; Ec. I.14. See also Gildersleeve's Greek Grammar for examples from Plato,
Isocrates, Herodotus, Euripides and Homer) and it regularly occurs in the Greek papyri. Some examples that Colwell gives are:
1) BGU I, 19 (a lawsuit record dated 135 CE), col. II, lines 4f:
"hOSA PROSHNANTO PA[TRI?] KWN PERI TON PROKEIMENON APO THS EU [D] AIMONIDOS DIAQHKHS . . . TAUTA METEINAI TOIS EKEINOU TEKNOIS. Compare Jn 1:12 with BGU II, 372 (official decree, dated 154 CE), col II, lines 19f "where EAN TIS occurs in the same construction" (Colwell, 38).
Other Greek papyri containing the CASUS PENDENS construction are BGU II, 523 (a letter), P.Oxy. II, 299 (a letter dated 1 CE) and P.Oxy.II, 268, line 2 (a repayment of a dowry, dated 58 CE).
I also recommend Light from Ancient Letters (Philadelphia: Fortress Press, 1986) by John L. White.