The expansion of space is entirely consistent with special relativity (the source of the "cosmic speed limit"). What relativity says is that the speed of light is consistent in all reference frames, which leads to all the phenomena you've heard about, such as time dilation, redshifting, and the upper bound on velocity. However, you have to understand that space and time are the same substance called "spacetime", and adding new space changes the basis of your velocity measurement (v = dx/dt). It's entirely possible that adding space between two regions can cause those regions to separate at a velocity faster than light in either reference frame, because space is the `dx` in the formula.
Another apparent violation of the speed limit occurs beyond the event horizon of a black hole. Space itself is drawn to the singularity faster than light.
Another apparent violation of the speed limit occurs beyond the event horizon of a black hole. Space itself is drawn to the singularity faster than light.