Absolutely! Projective geometry in which any two lines intersect is non-Euclidean.

Hyperbolic and Elliptic geometries came from different interpretations of the Fifth Postulate and this is why the are commonly labeled non-Euclidean. Projective geometry was an independent development but is as much non-Euclidean as the other two.

In addition, any non-discrete geometry is also non-Euclidean. So geometries may be non-Euclidean but for different reasons.

Quite often the Taxicab geometry is presented as one of the variety. I believe it's a misnomer. In fact, I do not think it's a geometry at all. It's a metric space, yes, but not a geometry. It violates the most common requirement of having a single line through any two points.