E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Mess = 4.
Nares says because at great dinners the company was usually arranged into fours. That four made a mess is without doubt. Lyly expressly says, Foure makes a messe, and we have a messe of masters (Mother Bombie, ii. 1). Shakespeare calls the four sons of Henry his mess of sons (2 Henry VI., act f. 4); and Latine, English, French, and Spanish are called a messe of tongues (Vocabulary, 1617). Again, Shakespeare says (Loves Labours Lost, iv. 3), You three fools lacked me to make up the mess. Though four made a mess, yet it does not follow that the officers mess is so called, as Nares says, because the company was arranged into fours, for the Anglo-Saxon mese, like the Latin mensa = table, mes Gothic = dish, whence Benjamins mess, a mess of pottage, etc.
Mess, meaning confusion or litter, is the German mischen, to mix; our word mash.