The speed limit of tardyon's (defined as particles for which v < c at all times) is obviously yes. Tardyon's are things like electrons, protons, positrons, antiprotons, etc. The are two other classes of particles. One is a Luxon for which v = 0 at all times (e.g. a photon) while the last one is a Tachyon for which v > c at all times. Tachyon's have never been observed so for all we know they don't exist. I read the argument for their existence and found it weak to flawed myself. That is just my personal opinion. But I doubt many physicists believe in the existence of Tachyons. However if they did exist then they are born moving faster than light and at best one accelerates it to as high of a speed as one wishes or decelerates it to a lower bound of the speed of light.
Best regards
Pete