A classic, massive Koine grammar is by A.T. Robertson (ATR). ATR’s book was used for many years as the reference book on Biblical Koine, and still is. As to comprehensiveness and sophistication it is the opposite of Zacharias’s book discussed above.
As one example, ATR has a section on the Koine language itself. (The numbers below are the respective pages on the respective sub-topic).
Κοινή: 17, 18, 21–4, 32, 46; chapter on, 49–74; term, 49; origin, 49; triumph of the Attic, 51; fate of the other dialects, 52 f.; influence of the dialects on the κοινή, 53; partial koines, 53; effect of Alexander’s campaigns, 53 f.; spread of the κοινή, 54–60; a real world-speech, 54–56; vernacular, 56; literary, 57 f.; the Atticistic reaction, 58–60; characteristics of the vernacular κοινή, 60–73; vernacular Attic, the base of the κοινή, 60–2; the other dialects in the κοινή, 62–64; non-dialectical changes in, 64 f.; new words in, 65; new forms of old words, 65 f.; poetical and vernacular words, 65; new meanings to old words, 66; i/a.d. the climax of the κοινή, 66; provincial influences in, 66–9; κοινή in Asia Minor and in Alexandria, 67 f.; in Palestine, 69; κοινή a single language, 69; personal equation, 69–71; résumé of the characteristics of the vernacular κοινή, 71–4 (phonetics and orthography 71 f., vocabulary 72, word-formation 72, accidence 72 f., syntax 73 f.); adaptability of the κοινή to the Roman world, 74 f.; place of the N. T. in the κοινή, 76–140, 152 f., 159 f., 161–3, 171; accent in, 228 f.; pronunciation in, 236–41; ad libitum in the book.
Robertson, A. T. (2006). A Grammar of the Greek New Testament in the Light of Historical Research. Logos Bible Software.
To find ATR’s teaching on kai we need follow this tree: Chapter 21, “Particles,” Part 5 “Conjunctions, Sub Part 1 “Paratactic Conjunctions,” Sub Sub Part (a) “Copulative,” Sub Sub Sub Part (ii) “kai.” It takes almost 1200 pages in his grammar to begin his systematic discussion of kai, as follows:
(ii) Καί. The etymology of this conjunction is disputed. Curtius3 makes it the locative case of the pronominal stem κα-, κο-, so that it would ultimately come from the same root as τέ (que). It would thus mean ‘in this respect,’ ‘this besides.’ Brugmann1 finds its original sense in κοινός, Latin co-, cum, Gothic ga. The idea would then be ‘together with,’ ‘in addition to.’ The Arkadian, South Achæan and Cypriote dialects use κάς and κά=καί. Whatever the origin, it all comes to the same thing in the end. It is by far the most frequent of all the conjunctions or other particles in the N. T. It is so common in fact that Moulton and Geden do not list it in their concordance. This in itself is in accord with the later Greek idiom, as Thumb notes in Aristotle and in the modern Greek and Moulton in the papyri. … But there can be little doubt that the extreme fondness for parataxis in John’s Gospel, for instance, is partially due to the use of καί in the LXX for the Hebrew וְ which “means a hook and resembles a hook in shape.” It was certainly used to “hook” together all sorts of sentences. There is not the same unity in the older Greek in the matters united as is true of τέ. Καί “connects in a free and easy manner” and the he Hebrew וְ still more loosely.
Ibid. pp. 1179-1180 [highlights mine]
What follows are ATR’s three primary categories of usage: “the adjunctive” (“also”), “the acensive” (“even”), and “the mere connective” (“and”).
ATR’S Adjunctive Use of kai: “also”
The Adjunctive Use (‘Also’). This is possibly the original use, though one cannot tell. It is thus like the Latin et-iam, English too (to)=addition to something already mentioned, and is common enough in all stages of the language. A good example of this use of καί is seen in Mt. 8:9…. The καί here points to Christ’s relation to the boy. The centurion, like a true soldier, does not say that he is a man who gives orders, but rather one who obeys them. He has the true military spirit and knows therefore how Jesus can cure the boy without going to see him. The καί is here very significant. Cf. …where the Golden Rule is applied to Christ’s hearers by καί. …. So then καί in the sense of ‘also’ occurs with nouns, pronouns, verbs, adverbs, conjunctions. It may refer to a word or a clause…. It is common for καί to sum up a sentence that precedes. For the relative and articular participle see the καί in the sentences in Mt. 5:39–43. Here καί balances the principal and the subordinate clauses. So in the apodosis of a conditional sentence we find καί as in Jo. 14:7. Cf. Heb. 7:26, where καί almost means ‘precisely,’ and Mt. 6:10, where it means ‘just so.’ Cf. Ro. 11:16….. Sometimes the καί seems to be redundant as in Lu. 11:1…. We may indeed have καί (‘also’) in both parts of the comparison, a studied balancing of the two members of the sentence as in Mt. 18:33….
ibid. p. 1180-1181 [Cf. is the abbreviation for “see also;” the “apodosis” is the outcome of a conditional sentence: “A complete conditional sentence consists of two clauses the protasis and the apodosis. The clause containing the condition is called the PROTASIS the clause containing the conclusion is called the APODOSIS.” quotation is Dickinson College Commentaries, though not specific to Koine}
ATR’S Ascensive Use of kai: “even”
The Ascensive Use (‘Even’). The notion of ‘even’ is an advance on that of mere addition which is due to the context, not to καί. The thing that is added is out of the ordinary and rises to a climax like the crescendo in music. Cf. Latin adeo. Cf. …Ac. 21:13; Ro. 13:5). This use of καί depends wholly on the context. Cf. Mk. 1:27, … (So Lu. 10:17). Cf…. Mt. 5:46 f. See further Ac. 10:45; 11:1, 20; Gal. 2:13. The use of καὶ εἰ belongs here. (Cf. 1 Cor. 8:5.)
ibid. p. 1181-1182 [highlights mine]
ATR’S Connective Use of kai: “and”
The Mere Connective (‘And’). The difference between καί as ‘and’ and καί as ‘also’ is very slight, whichever was the original idea. The epexegetic or explicative use of καί occupies a middle ground between ‘also’ and ‘and.’ Blass treats it under ‘also.’ Cf. Lu. 3:18,… where the “connective” force of καί is certainly very slight. So also Jo. 20:30, …. See further Jo. 1:16, … where the clause is an explanatory addition. Cf. (Ac. 22:25) … (1 Cor. 2:2) … (Ro. 13:11) καὶ τοῦτο (Latin idque) which is our ‘and that too’ where we combine ‘and’ and ‘also’ (‘too’) in the καί, (Heb. 11:12) καὶ ταῦτα (frequent in ancient Greek). See in particular Eph. 2:8, … where τοῦτο refers to the whole conception, not to χάριτι. The simple copulative idea is, however, the most common use of καί where words are piled together by means of this conjunction. Sometimes the connection is as close as with τέ. Thus … (2 Cor. 1:3); …. (Lu. 8:15). But the words may be very loosely joined in idea, as … (Mt. 16:1). Καί may be used to connect all sorts of words, clauses and sentences. … (Mt. 8:9). The use of καί after the imperative is seen in Mt. 11:29. The chain with καί as the connective may go on indefinitely. Cf. the four examples in Ph. 4:9; five in Ro. 9:4; the six in Rev. 7:12 (so 5:12). So we have καὶ ὅτι three times in 1 Cor. 15:4 (καί to connect ὅτι clauses). In Rev. 12–16 every paragraph and most of the sentences begin with καί. In fact it is true of much of the Apocalypse. …. We have noted the use of καί with τέ (τέ—καί Cf. Ro. 1:20). The use of καί—καί is far more common in the sense of ‘both—and’ as in Ac. 2:29,…. Cf. Mk. 4:41; Ph. 2:13; Ac. 26:29. Sometimes the connection almost amounts to ‘not only, but also.’ In Col. 2:16 note… (Lu. 12:38). ….Sometimes καί begins a sentence when the connection is with an unexpressed idea. Children use “and” thus often in telling stories and asking questions. C… Mt. 26:69 (and 73) like Et tu, Brute. See also Mk. 10:26…ι. So also Lu. 10:29; Jo. 9:36; 2 Cor. 2:2. Cf. also the use of καί in parenthesis as in Ro. 1:13,… The context gives other turns to καί that are sometimes rather startling. It is common to find καί where it has to bear the content ‘and yet.’ So Jo. 3:19; 4:20; 6:49; 7:30; 1 Jo. 2:9. The examples are common in John’s Gospel (Abbott, Joh. Gr., pp. 135 ff.). …. In Lu. 12:24 καί is almost equal to ἀλλά, that is, the context makes contrast. Cf. also Mt. 6:26 (οὐ—καί); Mk. 12:12; Lu. 20:19; Jo. 18:28. Tholuck1 so takes καί in Ro. 1:13 (the parenthetical καί). Sometimes καί seems imitative of the Hebrew וְ by almost having the sense of ὅτι or ἵνα (‘that’) as in Mt. 26:15; Mk. 14:40; Lu. 9:51; 12:15. In particular note … (as in Lu. 5:1, 12, 17, etc.). …Sometimes after καί we may supply ‘so’ as in … Mt. 5:15; …, Heb. 3:19. See also Ph. 4:7. This is a kind of consecutive use of καί. Cf. Lu. 24:18. The fondness for co-ordination in the Gospels causes the use of καί where a temporal conjunction (ὅτε) would be more usual. Cf. Mk. 15:25, … (Lu. 23:44). ….
ibid, p. 1182-1183 [highlights mine)