My initial list of dances for four looks as follows. I give the publication date, the title of the dance and the choreographer (if known).
1705 Le Cotillon (Anon.)
1706 Le Menuet à Quatre (Anon.)
1710 Le Passepied à Quatre (Feuillet)
1711 Mr Holt’s Minuet & Jigg
[c1713] Menuet à Quatre (Pecour)
[c1713] Rigaudon à Quatre (Pecour)
1716 La Gavotte du Roy (Balon)
1719 L’Italiene (Dezais)
1725 Cotillon Hongrois à Quatre (Dezais)
1725 L’Inconstante à Quatre (Dezais)
1725 La Blonde à Quatre (Dezais)
1725 La Brunne à Quatre (Dezais)
1725 La Carignan, Menuet à Quatre (Dezais)
1765 Le Quadrille (Magny)
1771 Passepied à Quatre (Clement)
1771 Allemande à Quatre (Clement)
There are also two dances for which we have no date of composition or publication:
La Blonde et La Brune (Anon. Source unknown, unless this choreography is the same as the Dezais dances above)
Minuet à Quatre (Pecour. In a manuscript collection dated 1751)
So, there are around 18 dances for four among the surviving notations
The next question concerns the sources for these dances, and what they might tell us about the status of dances for four in the 18th-century ballroom.