<p>I am printing Benchies at high speed, I successfully printed one at 300 mm/s. If I set the speed to 400 mm/s, the Y axis begins shifting around. This is usually accompanied by a banging sound.</p>
<p>In addition, the extruder motor occasionally clicks. When it clicks, the filament shoots back out a little bit.</p>
<p>Print settings:</p>
<ul>
<li>Infill: 100 %</li>
<li>Hotend: 200 °C</li>
<li>Bed: 60 °C</li>
<li>Material: PLA</li>
<li>Infill: Lines</li>
<li>Walls: 2</li>
<li>Top/bottom layers: 2</li>
<li>Speed: 400 mm/s</li>
<li>Jerk: 400 mm/s</li>
<li>Acceleration: 1000000</li>
</ul>
<p>I am running custom Marlin-based firmware on the stock mainboard.</p>
<p>The printer shakes my desk when printing like this.</p>

TL;DR: Don't do that.
Detailed answer: You need motion limit parameters that actually make physical sense, and firmware capable of executing a motion plan according to them. Your jerk and acceleration settings absolutely don't. Marlin's whole implementation of jerk is wacky (note: modern Marlin versions don't even use it but an alternative they call "junction deviation" instead) and likely to cause problems above very low values; I never was able to take it above 25 or so on Marlin without layer shifts. Acceleration is dependent on the stepper motor torque and the mass you'll be accelerating. For the Y axis, that's the bed, and it has enough mass you won't accelerate it above 12000 mm/s² or so, much less the requested 1 km/s² plus near-infinite acceleration from the extreme near-instantaneous 400 mm/s velocity change ("jerk").
The speed of 400 mm/s is achievable if you don't do it instantaneously. Stepper motors begin to rapidly lose torque beyond a certain speed due to limits on how fast the magnetic field can build up and be reversed, which has to happen for each step.
This calculator
can compute the limits if you know the properties of your motor. For the Ender 3 Y axis motor, the limit is around 425 mm/s or so if I'm remembering right.
For actual print speed, though, the hotend and extruder cannot keep up with anything nearly that high. 150 mm/s is about the limit with that hotend, and it might even be lower with a stock extruder. Fortunately, Benchy is mostly acceleration-bound, not top-speed-bound, so if you can get your acceleration profile right, you can still print quite fast.
Now the next limit you'll hit is Marlin. Marlin is... not good at high speeds and accelerations. Often the layer shifts you hit with Marlin aren't even physical limits but Marlin bugs. If you want to go fast, you need Klipper, not only because it lacks these step timing bugs, but because you need its Input Shaper feature to keep the high acceleration from tearing your printer apart (literally, vibrating all the screws out!).