Rules explicitly as written:
- Attack Rolls grant or revoke cover
- Ability Checks Pick a different (better) ability or (proficient instead of non-proficient) skill, set an easier/harder DC.
- Saving Rolls grant cover.
Remember: cover grants +2 to +5 AC.
Remember: many ability check DCs are really just someone else's passive score, so you can advantage/disadvantage the other guy, too, and shift the DC by 5, and be explicitly within the rules.
Reading between the lines
A circumstance bonus of ±5 or less is in line with the VERY few bonuses listed in the rules. Namely, Cover (+0/+2/+5 AC and Dex saves), Concealment (+2 to +5 AC) and advantage/disadvantage on passive ability scores (+5/-5).
Applying conditions may be equivalent. If the advantage to hit is overwhelming, then declare that the target is "effectively prone." If the disadvantage to hit is overwhelming, declare an automatic miss on anything but a 20. If the disadvantage to save is overwhelming, give advantage on the DC needed (it's essentially a Passive Ability Check at -2) for a +5 to the DC. If the advantage to save is overwhelming, put disadvantage on the save DC, reducing it by 5...
- Just say "You succeed" rather than worry about rolling with overwhelming advantage.
It's possible to do a number of things that not explicitly in the rules, but are well in line with the assorted class features and spells.
- Granting a single bonus die to the check total - in the same manner as the Bard feature Bardic Inspiration.
- Increasing an attribute by 2 for some reason - to a maximum of Attribute 20 - in line with a couple spells. Effectively a +1.
- Allowing a reroll on a failure, in line with Luck.
Invoking Optional Rules
Invoking optional rules on a single use basis can be a good option.
Technically, this includes switching to a better attribute and proficient skill, but is easier when the option to use skills with any attribute is used.
Invoke the rolled proficiency - this is generally a +0.5 bonus worth... but always leave this one to the player's decision.
Allow rolling 3d20 keeping the best 1. This does the least damage to bounded accuracy.
Allow standard inspiration to be used as bardic inspiration.
Have a pixie bard or the shade of a bard cast a boon upon the PC... for bardic inspiration of some die size.
Grant a bonus to damage.
Roll 1d20 & 1d24 or 1d20 & 1d30 instead of 2d20 when using "über-advantage". (Breaks bounded accuracy. Badly)
Advisoriam - Memento Morti (Advisories: Remember Death)
If you go beyond the standard bounds, things often get to the point where one should not bother to roll.
If you disadvantage the targets AC, and advantage the attack roll, you have almost ensured a hit... and bend the bounds of bounded accuracy a good bit.
If you allow a 3d20k1 for "über advantage", you just shoved the chances of crit from advatage's 39/400 (9.75%) to 1141/8000 (14.26%), but still allow for mandatory failure (1/8000). And at 4d20k1, 29679/160,000 (18.55%). But what you don't do is break bounded accuracy.
At a certain point, it's fine to just "say yes" or "say no" rather than bother with the roll.