Return of the Jedi
Max and his band originally were hired to perform as entertainment for the crime lord Jabba the Hutt at his palace on Tatooine. During this time, the band expanded to add several various alien musicians and singers to the group, including Snootles' backup dancers/singers in the Twi'lek Lyn Me, Rodian Greeata Jendowanian, and half-human/half-Theelin Rystall Sant.
One day, R2-D2 and C-3PO arrived at Jabba's palace with a message from Jedi Knight Luke Skywalker, offering to bargain for his friend, Millennium Falcon pilot Captain Han Solo's release in return for paying Jabba a decent amount in return, offering his droids as a gift to sweeten the deal, but upon suggestion from his majordomo Bib Fortuna, Jabba refuses and decides to keep the droids anyway, assigning R2 to serve drinks on his sail barge, Khetanna, while 3PO was made Jabba's personal translator/interpreter droid. Following acquiring R2 and 3PO, Jabba has Max and his band perform in celebration.
In the original movie, Max, Droopy, and Snootles perform the Huttese song, "Lapti Nek", while the Special Edition is extended with them performing "Jedi Rocks" with their larger band. During this time, Jabba's personal Twi'lek slave girl, Oola, performed to the music for everyone's entertainment, but then attempted to rebel and escape, trying to wrestle her chain keeping her restrained by Jabba away from him, but Jabba's grip held firm, as the angered crime lord secretly pulled Oola over the trapdoor to the Rancor pit as Oola begged and pleaded with Jabba. Once Oola was over the trapdoor, and despite a final plea from her, Jabba hits the switch to trigger the trapdoor, and Oola is dropped into the Rancor pit to her doom, interrupting Max and his band's performance. They can only watch from above as the helpless Twi'lek girl meets her end at the Rancor's voracious appetite.
Shortly after, Max and his band witness the arrival of the bounty hunter Boushh and his captive, Han's co-pilot, the Wookiee Chewbacca, who Boushh brought to claim the bounty on. When Jabba becomes angered at Boushh requesting 50,000 bounty for Chewie, and Boushh reveals that he's carrying a live thermal detonator grenade to blow everyone up if he doesn't get the bounty he requested, Max covers his eyes as he braces for the blast, but Jabba, impressed by Boushh's innovation and lack of fear, offers 35,000 bounty for Chewie, which satisfies Boushh, who disarms his grenade. As Chewie is taken away to be locked up in Jabba's dungeon by his Gamorrean Guards, Max and his band resume performing.
That night, they are part of an ambush by Jabba, who catches Boushh, really Princess Leia Organa, after she freed Han from his carbonite slab, with Max laughing with Jabba as he taunts Han over how he's no longer a good smuggler for Jabba after failing to pay off his debt to the crime lord. As Han is taken to be locked up with Chewbacca, Leia is brought before Jabba to be made his new slave girl to replace Oola.
Max is awoken the next morning when Luke arrives personally to offer Jabba one last chance to bargain with him, choosing either to be paid for the release of Luke's friends, or be destroyed. Jabba refuses to bargain again and sends Luke to face the Rancor, but Luke manages to kill the Rancor by impaling it with the door to its holding cell, leaving Max and everyone watching above in shock, and Jabba furious. Enraged over losing the Rancor, Jabba condemns Han, Chewie, and Luke to the Sarlaac in the Great Pit of Carkoon, having Max and his band join Jabba on the Khetanna to provide entertainment on the way to the execution site.
However, once there, Luke and his friends overpower Jabba's guards on the skiff, while Leia uses her chain to strangle Jabba to death, ending the crime lord's reign of terror, while Max and his band are forced to abandon the Khetanna before Luke and Leia destroy it using the deck gun and escape on one of the skiffs with Han, Chewie, Lando, and the droids.
Following Jabba's death and corpse being destroyed in the destruction of his sail barge, Max and his band parted ways, leading to Max eventually joining the Rebel Alliance.