The Max is a Prince and the New Power Generation video included on the 3 Chains O’ Gold home video.
Shooting took place at Paisley Park Studios in Chanhassen, Minnesota, likely in mid 1992 and re-edited later in 1993. The video is built from several distinct sequences: A performance of the song with the group (a photo taken during the shooting will be used for the album booklet), Mayte and Prince swinging their hips in chains, and video clips showing life on tour. Some snippets (without the audio) of the shooting were shown on the Act I TV-special, but the full video was not released until 1994.
The Max contains footage of a Diamonds And Pearls Tour show (presumably the same one in London footage for Live 4 Love was also filmed) and a show on the Act I Tour (presumably at the Fox Theatre in Atlanta in mid March 1993). Furthermore there are shots from the autograph signing session in Turtle’s Rhythm and Views in Atlanta March 1993, backstages clips and Prince and the band arriving at club Tramp (on Jermyn Street) in London from June 1992.
Interestingly the video as it was released on YouTube and iTunes in 2017 is a previously unreleased version than runs longer compared to how it was featured on the 3 Chains O’ Gold home video.