When I reach 2nd-level on my Warlock, I gain two Invocations of my choice. I can't choose both to be Agonizing Blast, can I? Or say this is possible, would this then cause two separate instance of Agonizing Blast to trigger?
Eg: Hit with Eldritch Blast, AB1 triggers get +CHA, AB2 triggers get +CHA. Total added is +CHA*2
Seems like a ridiculous question, but it must be asked.
There is nothing in the rules that say you can't take the same Invocation twice. However, there would be no benefit to taking an Invocation twice.
This is the "ridiculous" part of the question, the wording on each Invocation actually limit themselves to confer no benefit if taken twice as most Invocations are worded as:
Invocation Name
You can cast [this spell] once using a warlock spell slot. You can't do so again until you finish a long rest.
or
Invocation Name
You can cast [this spell] at will, without expending a spell slot or material components.
Both wordings confer no benefit to taking it twice because you can still only cast [this spell] once until you finish a long rest (or gain a new cantrip, which, again, there's no use taking it twice). Think of it as similar to the limitations on Extra Attacks which don't stack because the wording is you can attack twice. (Oh, I'm sorry, I thought the feature said EXTRA attack, not TWICE attack. A player of mine actually said this)
For the specific case of Agonizing Blast, when you take it the second time, you add your Charisma modifier to the damage. Sweet! Wait... Can't I already do that? Yes. Again, taking an Invocation twice gives no benefit due to the wording.
If the rules are indeed interpreted as: You can certainly take the same invocation twice but the second'll be useless, then taking Book of Ancient Secrets twice would be tantamount to saying: You can certainly take BoAS invocation twice, gaining 4 1st-level ritual spells, but you just wasted a precious class feature to gain the ability to cast an additional 2 1st-level ritual spells. Was it worth it?
There are no rules preventing you from taking it twice if you really want to but you will only get the bonus once.
When you cast eldritch blast, add your Charisma modifier to the damage it deals on a hit.
While you have two sources telling you to add your charisma modifier, your charisma modifier is the single value, not double. If your mod is +3, +6 is not your modifier.
A rule in a similar vein is the proficiency rules which only allow proficiency bonus to apply once even if you have multiple sources of proficiency, race and class for example.
This is ultimately a common sense rule, there are no direct rules that state you may or may not use such a combination.
