One dictionary says "two or more" and even cites a Samuel Taylor Coleridge example with three things:

From https://www.merriam-webster.com/dictionary/both :

> both conjunction —used as a function word to indicate and stress the inclusion of each of two or more things specified by coordinated words, phrases, or clauses prized both for its beauty and for its utility he … who loveth well both man and bird and beast — S. T. Coleridge