You can violate ρ ≥ 0 and 0 ≤ φ ≤ π just as much as r ≥ 0 and 0 ≤ θ ≤ 2π. The opportunity doesn't come up as much in 3D; for example, writing the area and volume elements as r dr dθ and ρ² sin φ dρ dφ dθ requires r ≥ 0 and sin φ ≥ 0 (but not ρ ≥ 0) because you need the absolute value. But if you want to parameterize a surface with φ and θ, then you might want to violate these, much like when you parametrize a curve with θ.
I am slightly confused when I see (r, 𝜃,𝜙) with the meanings of θ and ϕ reversed (a different convention). I would probably keep making mistakes when calculating the rotation :):):)
