For Max, I would use he/hims, they/thems, or whatever other pronouns Max would prefer. Max is a shortcut in and of itself. Maxwell, Maximilian, Maxine, or Maximus can all be Max.
If Max were to decide that Maxs' pronouns were Maxillaries/Maximilleficint, I would at that point likely just refer to Max as Max. As at that point I feel that what has been made are no longer pronouns, but situational proper nouns.
By a much more extreme example, if Max has a flowchart/spreadsheet of pronouns that are time/date sensative, such as changing pronouns according to the current astrological sign + day of the week/phase of the moon, Max is being called Max.
Step right up! Step right up! Grab a pitchfork and stab a Nazi!