There are plenty of empires in history that have had growth trajectories far more complex than "rise -> final fall".

Of particular note is China, which made falling and then regaining territorial extent a practical sport.

By that logic, Europe, Hungary, Austro-Hungarian Empire, Byzantine Empire, Roman Empire, and whatever kingdoms that were there and in all of Europe during and before that are all one empire that kept rising and falling all the time.

The history of China is perhaps not the history of AN empire, but rather a bunch of states/kingdoms, some of which every now and then managed to subjugate their neighbors and build an empire, for a while.