Would increasing the number of wheels of a Jumbo reduce the braking distance?
Typically, a little gain is obtained.

Larger airplanes use anti-skid technology. Anti-skid works by modulating brake pressure to ensure the tires never skid. It's important to understand the relation between a tire's load, brake pressure, and actual retarding force. First, look at this image : 

It shows how as you increase pressure and the wheel starts slipping a bit (turning at a rate slightly slower than when free rolling), the friction coefficient rises sharply. Then after the 10% slippage, the peak coefficient is reached and thus the retardation force reduces. Anti-skid aims to keep the slip raitio as close to 10% as posssible. Therefore the retardation force is maximized.

The brakes of airplanes are strong enough to fully lock the tyres, but this is detrimental (results in 100% Slippage, so maybe 20% retardation force loss). So they can and do maintain optimal slip, therefore using the entire available 'grip'.

Now what happens to this picture if you add wheels?


If the added wheel is not braked (like the nose wheels are) then you lose braking. Indeed, the braked wheels will have a reduced vertical load, so they will provide less retardation force. It's quite useless.
If we add braked wheels then we see the tyiniest bit of gain. Let's see why.


First look at this picture of tire load sensitivity (this one shows lateral force while cornering, but longitudinal force while braking exhibits the same features): 

What is important to note, is that as a tire gets more loaded, its capacity to generate friction decreases.

Now for a jumbo: When 20 wheels share 500 tons of load, each tire sees 25t. with a default friction coefficient of 0.8, each tire generates 20t retarding force, so total of 400t retarding force.

Let's add 2 wheels in there. Now each wheels sees 22.7t of load. Their friction coefficient could now rise to 0.82, therefore providing 18.6t, for a total of 410 tons. Certainly far of the 40t that could be naively expected from adding 2 braked wheels! Only the load sensitivity nets us a gain.

It then becomes the usual game of trade-offs. How much mass is spent on bigger landing gear and wheels and additional brakes, versus the gain of harder braking (and thus even stronger landing gear legs?)

Apparently the Airbus guys decided the trade stopped at 20 wheels (because 25t of load on a single tire is the maximum the ground could handle) but they didn't even bother to brake them all, if I remember well only 4 of the 6 wheels of the main boggies are braked! So if you wanted to improve brake efficiency:


Install better tires on braked wheels
Brake the non-braked main wheels
Make some smart aero changes to increase aero downforce &amp; drag
Add braked wheels (and prepare to house them in the main body... good luck!)
Brake the nose wheels (but that would be terribly hard because it was never designed for that)