The party evoker has a Shield Guardian.
In the last session he hit 14th level and obtained Overchannel.
It is clear to me that if he used Overchannel when casting a spell on the Guardian, to be stored in the Guardian, that this would count as one use of Overchannel for him for the day.
But it is not clear to me when the spell was re-cast by the Guardian whether it would obtain the maximum damage that the feature allows.
The guardian can store spells according to the following (emphasis mine):
Spell Storing. A spellcaster who wears the shield guardian's amulet can cause the guardian to store one spell of 4th level or lower. To do so, the wearer must cast the spell on the guardian. The spell has no effect but is stored within the guardian. When commanded to do so by the wearer or when a situation arises that was predefined by the spellcaster, the guardian casts the stored spell with any parameters set by the original caster, requiring no components.
On the one hand, Overchannel says "When you cast a wizard spell" and on the re-cast it is the Guardian casting the spell, not the Evoker, and the Guardian does not have the Overchannel feature.
On the other hand, the spell is stored "with any parameters set by the original caster", which some say "means any of the choices that would be made when the spell is cast", and this might include the choice to use Overchannel.
So would an Evoker's Guardian be able to store the spell specifically as Overchanneled for maximum damage, or would it emerge as a rolled-damage spell?
Best Answer
Probably not but ask your DM
As you already elaborated in detail, the rules do not clearly say so one way or another. If you can store overchannel in the Guardian depends on if you consider overchannel a "parameter" of the spell.
What counts as a parameter of a spell however is not defined in the rules. The only time the word shows up in the PHB is in the malleable illusions feature of the illusionist. There are zero uses of the term in the DMG. As there is no clear rule on this, you will need a DM ruling.
What is a likely meaning of "parameters"?
I personally would consider the parameters of the spell to be the things you inherently choose when you cast the spell, not some external feature you can apply to modify the cast spell. This is supported by the Shield Guardian casting the spell, not the original caster, and by Overchannel being a feature of the caster, not the spell, it says:
Emphasis mine - this sounds a lot more as if the overchannel effect is something the caster causes, not the spell.
Would it harm to allow it?
A maximally cooperative DM may differ and be more generous in their interpretation. What would be the consequences?
Firstly, this will allow to cast it on downtime days, and use it one more time per day without necrotic damage. That does not seem too bad.
Secondly, to allow storing the overchannel effect means you can pile on two overchanneled max damage spells in the same round. Max damage for a spell like Cone of Cold adds 28 points of uplift over expected raw damage, so you add in the range of 60 points to a nova round for taking out the end boss or a room of goons. That seems more serious.
Thirdly, I think most dangerous long term is setting precedent allowing external features to affect the spells stored. There are a lot of features out there, and more are being printed with every splat book - you never know when a player will come and ask equal treatment for something a lot more broken.
Ask your DM. (Or, if you are the DM, decide for yourself).