Arbitrarily large
A 20th level character with the Boon of Fate can add +1d10 to the ability check of one target within 60 feet as a non-action. Since Epic Boons are not " spells,
class features, feats, racial traits, monster abilities, [or] magic
items" (DMG errata) and no other text includes epic boons within the definition of 'game features', they are not subject to the DMG errata that broadened the prohibition on magical effects with the same name stacking to all 'game features'. Therefore, a character-- though limited to only one copy of the Boon of Fate-- can benefit from infinitely many applications of said boon on a single roll.
A 20th level Wizard can cast simulacro. With the Boon of High Magic they can do this via Desejo twice per day without needing material components. With the Boon of Spell Recall you can do it three times per day. With a Tomo da Língua Fervida they can do it four times per day. With more Tomes of the Stilled Tongue they can do it more times, though they will need to attune a new tomar after each casting.
A 20th level Wizard lacking a tome of the stilled tongue and epic boons can store a casting of simulacro em uma glifo de proteção. This does not make the simulacrum 'appear as close as possible... and attack' when the glifo is activated, because simulacro creates a friendly, rather than hostile, creature. After creating such a glyph, the wizard can regain spell slots without losing access to the simulacro soletrar.
Either way, a 20th level Wizard can create a simulacrum of themself able to itself create a simulacrum via Desejo. The wizard can then create another simulacrum, dispelling the first one but leaving the one it created unharmed, as the second simulacrum makes another copy of the wizard. This allows the simulacrum creation process to be exponential rather than linear in growth-- each surviving simulacra creates perhaps three other dying simulacra who make 1 surviving simulacra each, the whole process of which takes no more than 6 rounds. After 24 hours, as an example, such a wizard would have 3^67200 simulacra, or around 35 decmilliasescensexoctogintillion simulacra.
Unlike most checks, a Stealth check's total lasts "until you are discovered or stop hiding", and is reused against the Wisdom(perception) total of a chacter that is searching for you. Our wizard, then, can make a stealth check to hide from a rat but not the simularcra. The simulacra within range can add 1d10 each to the stealth check via their Boons of Fate, and then teleport out of the way via a contingência spell tied to a mudança de avião. More can then teleport in via an action, add to the check total, and then teleport out via contingência, all within each of their turns. With a sufficiently large bag of rats, then, to ensure a large number of initiative counts, even all 35 decmilliasescensexoctogintillion simulacra should be able to efficiently discharge their stealth buffs into you within a few rounds. That would give you approximately a + 175 decmilliasescensexoctogintillion bonus to your stealth check. Note that since Perception checks não carry over a total to new checks like this, you can't pump them up to astronomical heights in the same way-- if you are careful to protect against direct observation and have even just 10 full 60' spheres of simulacra buff your Stealth there's no way anyone is ever going to find you unless you give yourself up-- they can't get more of a bonus to Perception than you have to Stealth.