No.
The concept of Eevee can be summed up as:
An ordinary pet with no special abilities, gains full elemental powers upon exposure to a strong source of said element.
So my argument is basically,
they have covered everything remotely "elemental",
any more would be overdoing it, inappropriate and done just for the sake of it.
"omg lets expose my mammalian pet to the Bug-rock, now it suddenly became a full insect!"
Theyve done all the stuff you shoot with fancy coloured beams, and a light and dark duo. Things like Poison or Rock are just out of place in this.
I say, give us a new pokemon to deal with the rest of the types.
One that is indeterminate at first, but evolves into pokemon resembling different kinds of species (an insect, a dragon, a ghost...)
Or even more reasonable,
a humanoid pokemon with no specialisation that can fully turn into a "technique" type under certain conditions (Fighting, Dark, Psy..)