I hope you don’t mind but my pyramid didn’t fit the correct geometry as yours did - my steps were more shallow.
Anyway, when it came to doing the roof pillars, I did not have the “happy accident” when using the remove doubles.
So, after a bit of thought, this is what I did.
I removed the two edges from the middle of each of the top sides (at an angle).
This removed the vertices at the top also.
Then I could just use a sub-divide on the square roof which is now square and has no extra vertices or touching edges.
This does mean that the sides of the roof have lost some geometry hut, it seems it is easier to add than take away (dissolve).
The finished result before the further subdivision and pillar creation is attached.
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