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Aasimar (at least Scourge and Protector) get an ability that allows them to add their level in radiant damage to any damage roll they make, and the Celestial Warlock gets to add their Charisma modifier to any radiant damage they do.

Additionally, if that warlock has Agonizing Blast, that also makes their eldritch blast do additional damage equal to the character's Charisma modifier.

Would all three features stack (once per turn) on an eldritch blast that hits, so that it does extra damage equal to twice the warlock's charisma mod+level?

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My reading of all three abilities comes to the conclusion that while your aasimar transformation is active, one eldritch blast attack would have extra damage equal to your level + your Charisma mod, and the rest would just have your Charisma mod (from Agonizing Blast).

The Protector Aasimar's Radiant Soul trait (VGtM, p. 105) says:

[...] once on each of your turns, you can deal extra radiant damage to one target when you deal damage to it with an attack or a spell. The extra radiant damage equals your level.

The relevant portion of the Scourge Aasimar's Radiant Consumption trait is worded identically.

Secondly, the Celestial warlock's 6th-level feature, coincidentally also named Radiant Soul (XGtE, p. 55), reads:

[...] when you cast a spell that deals radiant or fire damage, you can add your Charisma modifier to one radiant or fire damage roll of that spell against one of its targets.

Eldritch blast does not do radiant damage, it does force damage, so the extra radiant damage from the Aasimar's racial trait would not trigger this feature.

The extra damage from Agonizing Blast would work fine though.

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No

The description of the Celestial Warlock's Radiant Soul feature says:

Starting at 6th level, your link to the Celestial allows you to serve as a conduit for radiant energy. You have resistance to radiant damage, and when you cast a spell that deals radiant or fire damage, you add your Charisma modifier to one radiant or fire damage roll of that spell against one of its targets.

The rule says you can add your Charisma modifier to one radiant or fire damage roll. But you aren't making a roll for either. The eldritch blast damage roll is for force. The other damage you are applying are flat values based on level and Charisma modifier. No fire or radiant damage rolls are involved, so the ability can't be applied.

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    \$\begingroup\$ It's also worth clarifying that even if the aasimar's racial trait involved a damage roll, the Celestial warlock feature wouldn't apply to it - the feature only applies to "a spell that deals radiant or fire damage", which eldritch blast is not (no matter what additional damage is dealt alongside the attack). \$\endgroup\$ – V2Blast Sep 2 at 6:02
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    \$\begingroup\$ @V2Blast I had thought about that, but you could argue that Radiant Soul/Consumption modifies the spell so that is does, in fact, deal radiant damage so the standard damage type for eldritch blast may or may not be irrelevant. If you think about it, chromatic orb is a spell that may or may not deal fire damage depending on the casters choice. That would make it into a specific casting case rather than a general spell damage rule. That was when I noticed that the Radiant Soul ability of the warlock requires and actual fire/radiant damage roll which isn't present in this case. \$\endgroup\$ – Allan Mills Sep 2 at 6:58

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