Nope. The reason why light speed is said to be a constant is because no matter how fast the observer is travelling light will still appear to be travelling at (about) 300,000 m/s in relation to the observer. This is the basis for all of the strangeness of general relativity like time/space dilation.
You can continue to go faster indefinitely, but you will never go faster than light speed. As you accelerate, the energy it requires to continue accelerating increases, and as your speed tends towards the speed of light, the energy required to continue accelerating tends towards infinity. According to the current knowledge of physics, it is impossible for a body with mass to travel at or above the speed of light.
You can do some reading about it
here.
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