A friend of mine played a one-shot and they were all told to make 20th-level characters. He made an 18th level monk tabaxi with 2 levels in Rogue. He tried to make his character as fast as possible. My biggest concern was Feline Agility being paired with Haste (cast by his girlfriend's sorcerer character).

Let's start by breaking this down a bit.

The tabaxi is an 18th monk, so he gets a +30 to his speed, making his walking speed 60.

Then he took the mobile feat- making his walking speed 70.

If this tabaxi was affected by the Haste spell (see below) his walking speed would double, so now it is 140.

The Haste spell says (PHB, pg. 250):

Until the spell ends, the target's speed is doubled, it gains a +2
bonus to AC, it has advantage on Dexterity saving throws and it gains
an additional action on each of its turns. That action can be used
only to take the Attack (one weapon Attack only), Dash, Disengage,
Hide, or Use an Object action.

The rogue's Cunning Action feature says:

You can take a bonus action on each of your turns in combat. This action can be used only to take the Dash, Disengage, or Hide action.

So far, no problem… but now he wants to dash… three times.

140 (Current base walking speed) + 140 (action used to Dash) + 140 (extra action from Haste) + 140 (bonus action Dash from the rogue's Cunning Action) = 560 feet.

And now he wants to use Feline Agility to make his total movement for the round 1120 feet.

The tabaxi's Feline Agility trait says (Volo's Guide to Monsters, p. 115):

When you move on your turn in combat, you can double your speed until
the end of the turn.

This feels extremely excessive (because I think that speed would be over 135 miles per hour), but usually, I care more about everyone having fun than being a rules lawyer. But I am curious:

Can Feline Agility and Haste's doubling of speed stack?