Kardaschev's level-4 civ is virtually unimaginable simply because at level 3, Galactic-level energy control, we have embarked on the virtual zenith of possible civilization, yet we're barely half-way along the scale. Here is the level of recognition of knowing all, because we have achieved the ultimate power; to manage a galaxy. Now, the challenge is to repeat the effort toward separate galaxies, but that is just expansion of wisdom without necessarily expanding knowledge.
The two are just about the same thing; knowledge and wisdom. One might say the distinction is levels of capability of perfection merely by repeated experience. It's like learning how to do a task once to ultimate perfection. Now, can we do it again? Repeat the performance? And then again, and then, still, again. That is the acqusition of wisdom, not just knowledge. How to use knowledge to its best effects. We may be able to stack an infinite number of stones, one upon another, but how stable are they? With experience of multiple efforts, stability will increase. That's true progress at this level of civilization.
Is it possible to achieve a higher level of civilization than this?
Yes; that is what levels 5 and 6 are for.