I used to live near a place that sold special clothes for ballroom dancing, though I never went inside.
From talking to ballroom dancers, I understand that they tend to like strong shoulders, high armholes, and a lot of ease in the blades (ie, in the back behind the arm hole), so the coat fits cleanly with the arms raised. I believed I've heard it posited that one of the reasons Fred Astaire wore Anderson & Sheppard was that their house style of (you guessed it) high armholes and ease in the blades was especially suited to dancing.
I know some ballroom dance scenes are more open than others, and getting a gentleman to share the name of his tailor can be fraught, but I would suggest asking someone in your area for a recommendation. I'm sure there are tailors who wouldn't get your request, tailors who'd say "yeah, sure!" and take a stab at it, and tailors who are experts at cutting for dancers.
When I went out as part of a class I took, I left my suit jacket on a chair and danced in shirtsleeves. Most of the gents dancing wore shirts (generally rather fitted), or tailored vests (either a fancy, Favourbrook-type vest or 2/3rds of a three-piece suit), as I recall.