The speed of light is the same as measured in any reference frame.  So if you run away from a light source the light will always pass you.
If you speed up, you will still see the light pass you at the speed of light.  This is true no matter how many times you speed up.
The event of you being passed by a beam of light is something that everyone, in every reference frame, can agree on.  As such, everyone will observe that you are traveling at less than the speed of light.