This question already has an answer here:
Critical hits double all the dice rolls. Since Superiority Dice are dice rolls too, do they get doubled on a crit? That is, if a Fighter attacks, rolls a 20, and decides to use a combat maneuver, do they roll 2d8 for bonus damage?
Case in point: a Rogue3(Assassin)/Fighter3(Battle Master) multiclassed character deals a surprise round. Since they auto-crit due to Assassinate if they hit, they can also tack on a maneuver to add a guaranteed 2d8 damage (assuming the maneuver adds that damage in), on top of the 6d6 damage from sneak attack.
Related: Does a Critical Hit when tripping also double the Superiority die?, but I don't think it's a duplicate as this is concerning a more specific scenario with a multiclassed character.