Can a fighter use Indomitable multiple times on the same save?

Question

Our fighter, Fred, is a high level fighter with multiple uses of the Indomitable feature:

Beginning at 9th level, you can reroll a saving throw that you fail. If you do so, you must use the new roll, and you can’t use this feature again until you finish a long rest.

You can use this feature twice between long rests starting at 13th level and three times between long rests starting at 17th level.

Let's suppose Fred is targeted by the Hold Person spell. Fred rolls a 5 and fails the save. Fred uses one use of his Indomitable feature, to reroll the save, but still fails. Can Fred expend a second use of his Indomitable feature to reroll the save again?

Also, does this answer hold for the Champion and Warlord NPCs?

Indomitable (2/Day). The champion rerolls a failed saving throw.

Indomitable (3/Day). The warlord can reroll a saving throw it fails. It must use the new roll.

Answer 1

A fighter cannot use multiple uses of Indomitable on the same roll

The main limitation, as seen in the text you quoted, is that you "must use the new roll" when using Indomitable. If it were possible to use Indomitable a second time on that same roll, then you would not be using that roll, and therefore violating the constraints of the feature.

Note that this remains true even in situations where the Fighter has Advantage or Disadvantage on their Saving Throw; even if the rerolled die is too low (with advantage) or too high (with disadvantage) to affect the final result, you're still only permitted one reroll, per the general rules about Advantage and Disadvantage, and how rerolls interact with them:

When you have advantage or disadvantage and something in the game, such as the halfling's Lucky trait, lets you reroll or replace the d20, you can reroll or replace only one of the dice. You choose which one. For example, if a halfling has advantage or disadvantage on an ability check and rolls a 1 and a 13, the halfling could use the Lucky trait to reroll the 1.

―Advantage, Player's Handbook, pg. 173

In this context, the Indomitable feature is being applied once (and only once) to the entire roll, which allows one of the two dice to be rerolled.