I discovered this glitch while chasing sub-9. It seems highly unlikely to be useful in saving time in a run, but can be useful for exploring the arena for potential routing, or even creating challenge runs where you have to play against multiple Doofs. It's a serious challenge just to be able to survive long enough to summon 3 Doofs in level 3!

In the Doof arena, there is an invisible wall placed just at the left edge of the screen. However, a double jump leftwards from the left platform can get you over this wall. From there, you will not be able to see Perry, but can still control him. Due to the walls very close to you, it takes some practice to get a feel for controlling Perry in this state. Your best bet is likely to hold down for a few seconds to get to the ground. On the ground, you can move left to re-trigger the cutscene.

When the cutscene is re-triggered, a second Doof will appear. However, the original will not, and will continue to attack. For this reason, it is often difficult to survive through this cutscene, and it is recommended to begin with full health, even in level 1, and this is not always enough to survive, especially in later levels.

If you do die during the cutscene, an interesting glitch will occur when you try to respawn. Perry will be invisible, and the cutscene trigger can't be triggered. There will also be black bars at the top and bottom of the screen. You can still control Perry as normal, the camera still moves as normal (although it looks and feels much stranger as seems to follow nothing), and generally most things work as normal. However, with no way to trigger the cutscene, there is no way to beat the level. Interestingly, however, it also means that you camera is no longer fixed in the arena and a number of areas previously unseeable can be seen.

If you get past the cutscene, you're now in a battle with two doofs. Getting health ASAP will be key to surviving. Once you've done that, you can defeat the doofs independently. Defeating either is sufficient to beat the level. Note that they will both attack, but you will also get twice the supplies. Perhaps the largest struggle will be that you will also get twice the "resets," crippling the rate at which you can do damage. Staffs can be especially powerful in these fights, as you can potentially get four hits per throw, two on each doof.

If you happen to die right at the end of the cutscene, the animation of the black bars disappearing up and down will repeat until you respawn.

In theory, you should be able to die after defeating a doof. I'm not sure what happens in this scenario.