Example
There is this thing called Zalgo Text which pushes this to the extreme. Here is the first grapheme cluster of the example. It consists of 15 code points: the Latin letter H and 14 combining marks.
H̡̫̤̤̣͉̤ͭ̓̓̇͗̎̀
Although this doesn't show up in normal text, it shows that a “character” really can consist of an arbitrary number of code points
