well if you accelerate the inside accelerator, to near C, then to the observer it will appear to be going at near C.
if you also had a particle that was going at near C in the inner accelerator, relative to the inner accelerator, then to the outside observer it would look like it was going barely faster than the accelerator at all (think of time dilation in the accelerator for example) -> and will never reach C
hopefully that makes sense to you