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 18^th-century ballroom.