That's kindof BS...
Mass doesn't expand infinitely nor is there a speed threshold of energy as far as our current understanding of physics goes... This is a simplistic bookkeeping trick that attempts to account for limited acceleration near the speed of light (since F=ma, for a given force, you get less "a" if you somehow fudge 'm' to increase as you approach the speed of light). General relativity explains this much better by having any mass or energy actually distort space time so that you don't ever need this overly simplistic bookkeeping trick (which has unfortunate anomalies like rest-mass and photons having no rest mass, but momentum).
In your own frame of reference, you can accelerate as long as you have the energy to do so. The problem is that from an external observer's frame of reference despite your apparent acceleration from your frame of reference (you think you are going faster and faster), your time dilation factor relative to the observer means it doesn't observer you exceeding the speed of light, The observer thinks your acceleration (dv/dt) is asymptotically approaching zero as you approach the speed of light. Even though you have been accelerating all the time, you don't teleport relative to the observer (although the observer will think you were moving very, very fast, but not faster than light), but if you were to get back to the same frame of reference as the observer, you will have noticed your observer has experience quite a bit more time than you have (this is the origin of the twin paradox of special relativity).
From your special relatively frame of reference, you moved very fast (because you experienced less time for the distance you appeared to travel), but from the observers point of view, more time was experienced, so the velocity never exceed the speed of light. The way this is book-kept for is usually lorenzian length contraction. As you approach the speed of light the distance you observer to traverse over a unit of your time is shorter, so when you divide the distance by your time, you also don't observe that you went faster than the speed of light.
Of course if you could somehow create say a warp drive (or some other FTL transport), to a third party observer, you might appear to be in two places at once, and/or it would appear like time transport, but many folks thinks it is really possible to do this. Creating such a warp disturbance (actually warping space time around you) would likely require a very, very large, but not infinite amount of energy to maintain a negative energy-density around you. It is hypothesized you could not do this w/o some sort of pervasive zero-point energy source or creation of a type of exotic matter to sustain the required region of negative energy-density.