καί τοι
A.
and indeed, and further, freq. in Hom. with one or more words between, Il. 1.426, al.; καὶ σύ τοι E. Med. 344; καὶ τἆλλά τοι X. Cyr. 7.3.10: once in Hom. as one word, Il. 13.267.
II.
after Hom. usu., and yet, to mark an objection introduced by the speaker himself, freq. in Rhetorical questions, καίτοι τί φημι; A. Pr. 101; κ. τί φωνῶ; S. OC 1132, cf. Isoc. 4.99, etc.: without a question, κ. φύγοιμ’ ἄν E. Cyc. 480; κ. καὶ τοῦτο . . D. 4.12, 18.122: strengthd., καίτοι γ' Ar. Ach. 611, E. Fr. 953.10, X. Mem. 1.2.3, Ph. 1.274, etc.: mostly separated, καίτοι . . γε E. Or. 77, Ar. Ra. 43, X. Mem. 3.12.7, etc. (καίτοι is f.l. in A. Eu. 849); so καίτοι περ v.l. in Hdt. 8.53.
III.
with a participle, much like καίπερ, Simon. 5.9, Ar. Ec. 159, Pl. R. 511d, Plb. 22.8.13, Phld. Ir. p.22 W., Luc. Alex. 3: once in the Att. Oratt., Lys. 31.34; also καίτοι γε διαχλευάζων Pl. Ax. 364b.