Types we already have overlap as well. Rock and Ground are essentially the same thing, yet Pokemon made it into two separate type elements with different weaknesses and strengths. Grass is almost always associated with Earth elements outside of Pokemon, so we have 3 parts to 1 element in a type.
Water and Ice are usually associated in one element as well. They like Ground and Rock have their own weaknesses and strengths that work fairly well.
Overlapping probably wouldn't be so much of an issue.
If a new type is made, I'd prefer another elemental type, like say wind. Flying type is associated but flying type itself is not wind. A lot of wind based attacks are not flying typed and the only two known Pokemon based off wind are Grass/Dark and Water typed.