If neutrinos have mass and travel very close to the speed of light, could one not exceed c in reference to the other if they were the only two objects in the frame of reference?

It seems that if two space ships are travelling opposite directions at 10mph, its just as correct to say that one is stationary and the other is travelling at 20mph away from it. Although this must be incorrect thinking on my part. Because I know any object with mass cannot exceed c in any frame of reference.

That would be an indictment of all of relativity if correct. Fortunately it is not.

In relativity, when switching reference frames, the formula to transform velocities is not simple addition. The addition of velocity formula for two speeds u and v is (u + v)/(1+uv/c^2), which stays below c for all reference frames even if u and v are close to c.

Note that, for low speeds like 10 MPH, the simple addition rule is an excellent approximation, and the relative speed will be very, very close to 20 MPH. When you get to things moving at almost c, though, the approximation has very thoroughly broken down.