Ideas to tune for 300 % speed
extruder clicking means you're getting backed up, grinding.

Make the hotend hotter so you can melt filament 3X faster than expected; most materials have quite a range; aim high.
Slow down the cooling fan; a lot of them can cool the hotend.
You have a silicone boot on the nozzle? that will help some.
Use a larger diameter nozzle to reduce backpressure and allow thicker layers.
Try cranking the feed rate

Lastly, consider that you simply might not get acceptable results pushing speed THAT much.