SPOILER WARNING: DO NOT READ IF YOU HAVE NOT PLAYED DRAGON AGE:ORIGINS OR BG3 FULLY
The closes example to how this could be solved is in Dragon Age: Origins you had to chose between Alistair & Loghain but there was a way to keep both alive (but lose Alistair as a companion so not the best example) where if you went through Alistair's personal quest with his half sister you could harden him after the encounter with Goldanna by choosing a dialog options then later affirm it in the party camp which slightly changes his character slightly similar to Astarion when he ascends if you never played Dragon age.
With him hardened if you chose for him to rule with Anora you can spare Loghain from execution but Alistair leaves the wardens (and the party) to become king.
One way I think this could be solved for BG3 is to have a dialog option when you get back from retrieving the Orthic Hammer and he Psionically talks to you which opens the Emperor up to working with Orpheus.
"We could Persuade Orpheus to work with us" which will require high roll maybe 20-25 or something to that effect then after the encounter with the nether brain in the astral prism (When we know a mindflayer is required) if that roll failed the emperor will straight up refuse to work with Orpheus but if id did not fail a low roll requirement to persuade him to allow us to free Orpheus and have the emperor.
but there are probably better ways of doing it which I can not think of.
