Mugen is Rei's partner—a card known as Mugendra in his true form. He's not particularly fond of Ian, though they manage to work together when needed.
Mugen came into Rei's life after Rei had already acquired Ultimate-Siegfried and Ultimate-Odin, so he was never around for Rei's earlier history. That said, he's developed an obsession with Magical Star that borders on extreme. His fandom got so intense he dropped a fortune on one of her figures, basically draining the entire crew's funds. To earn money back, they took work as bodyguards for what they thought was Magical Star's first ribbon—except it turned out the person holding it had stolen it in the first place. Once they recovered the ribbon, they learned Magical Star would actually be visiting the planet they were on.
Plans to return the ribbon fell apart pretty quickly when Mugen literally crashed into Watari, damaging the bag in the process. Worse, Mugen discovered that Watari and the rest of the Triumvirate had kidnapped Magical Star. He wanted to fight immediately, but Rei stepped in instead and won the battle. The problem: Rei sacrificed Mugendragon to summon Ultimate-Kingtaurus for the win, so Mugen never got his moment. At least he managed to return the ribbon to Magical Star afterward, which made her happy.
Ultimate-Siegwurm-Nova had some kind of strange effect on Mugen when Rei first obtained it, but the issue cleared up once Rei summoned him in actual combat. Eventually Mugen evolved all the way to Ultimate-Mugendragon, and he finally got his moment—delivering the finishing blow in Rei's fight against Nakes.
Content compiled by AnimeList.moe from publicly available sources.