Laudator Temporis Acti

Grammarians classify Latin -que and Greek τε as correlative conjunctions. "Both ... and" is the usual literal translation. The number of conjunctions and the number of things joined are usually two, but there are exceptions. In a list that is not intended to be exhaustive, Richard John Cunliffe, A Lexicon of the Homeric Dialect (1924; rpt. Norman: University of Oklahoma Press, 1963), s.v. τε, cites the following triplets (tr. A.T. Murray, with italics representing the things joined by τε in Greek):

• Iliad 1.70: ὃς ᾔδη τά τ᾿ ἐόντα τά τ᾿ ἐσσόμενα πρό τ᾿ ἐόντα (who had knowledge of all things that were, and that were to be, and that had been before)
  
• Iliad 1.177: αἰεὶ γάρ τοι ἔρις τε φίλη πόλεμοί τε μάχαι τε (for ever is strife dear to thee, and wars and fightings)
  
• Iliad 2.57-58: μάλιστα δὲ Νέστορι δίῳ / εἶδός τε μέγεθός τε φυήν τ᾽ ἄγχιστα ἐῴκει (most like was it to goodly Nestor, in form and in stature and in build)
  
• Odyssey 2.120: Τυρώ τ᾽ Ἀλκμήνη τε ἐυστέφανός τε Μυκήνη (Tyro and Alcmene and Mycene of the fair crown)
  
• Odyssey 5.260: ἐν δ᾽ ὑπέρας τε κάλους τε πόδας τ᾽ ἐνέδησεν ἐν αὐτῇ (and he made fast in the raft braces and halyards and sheets)
  
• Odyssey 6.151-152: Ἀρτέμιδί σε ἐγώ γε, Διὸς κούρῃ μεγάλοιο, / εἶδός τε μέγεθός τε φυήν τ᾽ ἄγχιστα ἐίσκω (to Artemis, the daughter of great Zeus, / I liken you most in looks and in stature, and in form)
  

Liddell τε Scott τε Jones τε give some more examples:

τε may be used three or more times, ἔν τ' ἄρα οἱ φῦ χειρί, ἔπος τ' ἔφατ' ἔκ τ' ὀνόμαζεν Od.15.530, cf. Il.1.177, 2.58, A.Pr.89sq., B.17.19sq., Lys. 19.17, X.Cyr.3.3.36.

A Latin example with -que is Terence, Adelphoe 300-301: auxili nihil adferant, / quod mihique eraeque filiaeque erilist (they would bring no help [for the trouble] that is upon me and my mistress and my mistress' daughter).

Similarly in English, "both ... and" usually join pairs of nouns, but with an extra "and" there can be a triplet. See R.W. Burchfield, The New Fowler's Modern English Usage, 3rd edition (Oxford: Clarendon Press, 1996), p. 114:

If language behaved like a simple mathematical system, the illogicality of using both of more than two items would be immediately apparent. In practice, both is almost always used with two homogeneous words or phrases: both the people and the land; both by day and by night; he both loves and hates his brother; both now and evermore; etc. From the 14c. onward, however, it has been used 'illogically' in conjunction with more than two objects: both man and bird and beast (Coleridge, 1798) and both Chaucer and Shakespeare and Milton (De Quincy, c1839) form part of an array of examples presented in the OED.

Related post: Either ... Or.