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I was thinking there are some abilities that should be innate to the Pokémon (like Levitate or even Sturdy).
I still find odd to find some Pokémon that because of their nature they should be levitating but after they have other (for instance Bronzong) and there are others that I think they should be levitating but I also think they should have other innate abilities (Magnemite line should have levitate, but also Magnet pull)
My idea is to divide abilities into "innate/physical abilities" and "special abilities", so some Pokémon could have two abilities because of its nature. One physical and another one special, or even two physical (Magnezone for instance could have Magnet Pull and Analytic, or even Levitate if this was a possibility).
Also, another idea is that these special abilities could be "taught" while the innate ones cannot be removed or changed, because it is what their body do just for existing. For instance, "Truant" would be a special ability by default, but could be re-educated after certain level. Another example could be Pelipper, whose innate ability by default would be "Keen eye" but it could be taught how to summon rain (Drizzle) or how to cure itself with the rain (Rain Dish).
Of course some abilities would have to be redistributed to not create OP cases.
And not every Pokémon must posses access to both abilities. Some of them will only have "innate abilities" and some of them only "special abilities.
I created a draft list of abilities:
