Will mixing different brands of toothpaste make for a super tooth paste?

I have wondered this for years every week, when I shower ;-) but always forget to ask.
The tooth pastes that I buy are never the same brand, I buy what is on offer or what looks appealing or what I remember from earlier use.
Sometimes there are two or three packages on the shelf in my bathroom.
Now I wonder, looking at what they do (some have fluroids, some have whiteners, others work to avoid calculus, and others still are good for your gums, etc.), will/would mixing those different products/brands deliver one super tooth paste that fights all areas and is beneficial to your whole set of dentures?
Or will I get a paste that doesn’t work at all?

The same question I have for shampoos, by the way…