In discussions for exhaustion (like this one or this one), bandwidth is spent on what happens if exhaustion would exceed six levels.
The definition of exhaustion also says:
An effect can give a creature one or more levels of exhaustion, as
specified in the effect’s description.
However, I was not able to find any effect that would add more than one level of exhaustion at a time in the core rules. Is there any published effect (from a spell, magic item or monster, or any other source) that is able to do this?
Best Answer
Be tired and thirsty
There's a weird little rule tucked away in the food and water rules in the PHB (Chapter 8 > The Environment > Food and Water) which says that if you already have any exhaustion, you suffer two levels of it from lack of water.
Run yourself into the ground
This requires a bit more setup and lands into a slightly ambiguous territory, but using the chase rules from the DMG (Chapter 8 > Chases) it's possible to gain two levels (or more) at the end of your turn. In short, if you've already taken a bunch of dashes in that chase, each one you take forces a Con save with failure gaining you an exhaustion level at the end of your turn. So, if you Dash twice on a turn (eg. rogue, monk, fighter) you will be subjected to two such saving throws, for as many levels of exhaustion.
There's some ambiguity as to how simultaneous this is. Both levels are gained at the end of the same turn, though behind separate saving throws. Whether they're fully simultaneous will depend on what goal they need to simultaneous for. You can certainly jump from exhaustion 4 to dead without getting stuck at that pesky speed of 0, if that was your goal for some reason.
Hot teeth
Teeth of Dahlver-Nar is an artefact from Tasha's Cauldron of Everything. Skipping over how the item works, we want effect number 19 which allows us to make a whopper breath attack at the low-low cost of two exhaustion levels.
Break a Vow
The Broken Vow sample curse (in the Horror Adventures chapter) from Van Richten’s Guide to Ravenloft includes:
Adventures and Monsters
I'll cover these briefly as they're already covered by Tobias F's excellent answer.
A Loup Garau's lycanthropy being lifted (Van Richten’s Guide to Ravenloft)
The Mystery Mine from The Wild Beyond the Witchlight includes after failing a sufficient number of saving throws
The Zikran’s Zephyrean Tome from Candlekeep Mysteries includes exhaustion as the fail state for a specific climbing check