Meryl, isn't there a stunningly beautiful and sad quartet in Cosi Fan Tutti?...seems like there'd be more than one opportunity for something like that in BBM, whether or not the characters know they're all singing at the same time.
Yes, the quartet in
Cosi comes near the end, after the ladies discover they've been tricked into falling for each other's fiances. They go back to their original lovers, and all four sing a harmonious toast to their upcoming marriage vows. But one of the four, Guglielmo, can't swallow his anger entirely, and his vocal line becomes a jumpy and emotional counterpoint to the others.
Off the top of my head, I can't think of a quartet in the standard rep that uses the situation of two couples onstage at the same time, who are actually in different physical locations, with two true lovers thinking of each other while they're with someone else. It would be an utterly cool scene to do.