(uncommon) One's spouse's brother-in-law (one's spouse's sibling's husband), especially one's wife's sister's husband; either of two (or more) men who marry sisters, in relation to the other; the brother of one spouse in relation to the siblings of the other spouse.
2008, Daniel Bornstein, David Peterson, editors, Florence and Beyond: Culture, Society and Politics in Renaissance Italy, page 350:
Knowing that he would be susceptible to the arguments of his persuasive co-brother-in-law Antonio de' Medici, Saminiato tried to avoid his company.
(uncommon) One's brother-in-law's or sister-in-law's brother; that is, one's sibling's spouse's brother; either of two (or more) men whose siblings are married to each other.
The term is generally used in translation in South India (Karnataka, Tamil Nadu, Andhra Pradesh) where the local language makes the distinction. In common speech in traditionally English-speaking countries, brother-in-law may be used.
The primary usage is for one's wife's sister's husband.
Languages that have words for this relationship that are distinct from the word for brother-in-law. Not all are attested to have the second meaning above, though this may sometimes be an oversight.
Armenian: քենակալ (k’enakal) (wife's sister's husband); (less precisely)փեսա (p’esa) (husband of any close relative, including one's sister or sister-in-law)
Korean: 동서 (同壻) (dongseo) (with siblings of the same sex: a man's wife's sister's husband, or a woman's husband's brother's wife, but not cheonambu a man's wife's brother's wife)