[MNDude]

The best way to prevent getting finger printed would be if your browser randomly browses thousands of different sites in the background, so it’ll clutter up the real data with garbage.

[ShadowAce]

It's the website that does the fingerprinting.

What other sites you may be browsing at the same time would not have an effect on what the browser is doing at that site.

[Bloody Sam Roberts]

I have an extension that does something like that...AdNauseum.

Essentially, AdNauseam quietly clicks every blocked ad, registering a visit on the ad networks databases. As the data gathered shows an omnivorous click-stream, user profiling, targeting and surveillance becomes futile.