The standard says this:

In general, two <window function>s are computed independently, each one
performing its own sort of its data, even if they use the same data and the same <sort specification list>
...
Nevertheless, the user may desire that two <window function>s be computed using the same ordering
...
Two <window function>s are computed using the same (possibly non-deterministic) window ordering of the
rows if any of the following are true:

• (3 long clauses)

This is a good reason to implement an optimization:

if window functions W1 and W2 use compatible sortings, 

  they must share the filesort() call

Let's call the above *filesort sharing*.

The second step would be to share the "scan through the filesort result and compute the window function" step. Sharing the scan between window functions ought to give a speedup, because

• we can compute values of all window functions and call h->update_row once (instead of many times)
• It is more cache-friendly to do things in one pass, not in many.

A question: should the scan be shared across all window functions or only those that have identical PARTITION BY clause?