The Maxixe (pronounced "Masheesh") gained some popularity in the teens but was never as universally embraced as the One-Step, the Waltz or even the Tango. It is a more or less a Latin dance, the predecessor of the Samba. The basic step (for the man, woman is opposite) is Left forward, Right forward, Left back, Right back. The steps are small and rapid. Spins are a popular variation.
It is essentially a One-Step variation, with a focus on the feet moving very rapidly as they step to every beat in a fast-tempo piece of music.
In this video, Vernon and Irene Castle demonstrate it.