Absolute Stealth (5e Optimized Character Build)
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At most +156. This does not include the 20 from the d20. The maximum rolled result would be 176.
Your character must have... At least 10 levels in Ranger, to get Hide in Plain Sight. At least 1 level in Rogue, or 3 levels in Bard, to get Expertise. At least 6 levels in Warlock (The Fiend), to get Dark One's Own Luck. 20 levels total. Dexterity score of 20. You can start lower, but you need 20 by 20th level. Wisdom and Charisma scores of 13+ to meet multiclassing prerequisites. Boon of Luck, Boon of Undetectability, and five Ability Score Improvements as epic boon alternatives.
Your magic items must include... Stone of Good Luck (requires attunement) Ioun Stone of Mastery (requires attunement)
Your 4 allies should include... A bard of at least 14th level, who uses a d12 for their Bardic Inspiration die. A Wild Magic sorcerer of at least 6th level, for their Bend Luck feature. A Circle of Dreams druid of at least 6th level, for their Hearth of Moonlight and Shadow feature. An Artificer (from Eberron: Rising from the Last War) of at least 7th level, with 20 Intelligence, for their Flash of Genius feature and the guidance cantrip. Someone wearing the Lost Crown of Besilmer (from Princes of the Apocalypse) Each of your four allies has 20 levels total, and a Boon of Fate.
The Math: Start with your character's Dexterity modifier. Without magic items, you can get 20 Dexterity. You then ask your DM for five Ability Score Improvements (listed as epic boon alternatives), raising your Dexterity to 30. Your Dexterity modifier is +10.
As a 20th level character with the Ioun Stone of Mastery, your Proficiency bonus increases by 1, from +6 to +7. And with Expertise in Dexterity (Stealth), you add your Proficiency bonus twice to the stealth check. This becomes a +14 bonus.
Also, your Boon of Undetectability adds +10 to Dexterity (Stealth), and your Stone of Good Luck gives an extra +1 to ability checks. So far, you have a total +35 Stealth bonus, without any temporary or situational benefits.
But wait, there's more! As a Ranger, you cast pass without trace, which gives a +10 bonus for the next hour. Then you take a minute to camouflage yourself via Hide in Plain Sight, which will give you another +10 bonus.
This next hour will be a short rest. Your druid ally uses Hearth of Moonlight and Shadow to give everyone a +5 bonus to Dexterity (Stealth).
Your bard ally gives you a d12 Inspiration die. And if they're wearing the Lost Crown of Besilmer, they can use their next bonus action give you another +1d6.
The Artificer ally casts guidance, which will add +1d4 to the check. Also, the Artificer has five Ability Score Improvements as epic boons, which boosted their Intelligence from 20 to 30. When you make the check, they use their Flash of Genius feature to add their Intelligence modifier of +10.
If your Wild Magic sorcerer ally can see you, then their Bend Luck feature can add +1d4 to your check. The sorcerer should then run away and hide elsewhere, lest they randomly explode and accidentally reveal your location.
Both the Dark One's Own Luck feature and your Boon of Luck each add +1d10. Your four allies' Boons of Fate each add another +1d10.
The total bonus is +(10 + 14 + 10 + 1 + 10 + 10 + 5 + 1d12 + 1d6 + 10 + 2d4 + 6d10) = 176 maximum (156 in bonuses), and 128 on average rolls.