I read a magazine article a few years ago about
hundreds of mummies stacked in the Cairo museum's basement.
The museum said they didn't have room in the museum for them.
Zahi Hawass said that they were trying to fix the problem.
What is being done? I haven't found any new articles on the subject.

They are constructing quite a few new museums around Egypt and moving certain artefact to the new museums. Whether or not this is what's been done with the mummies, I'm not sure, but it's certainly a possibility.

That's probably correct, DoS.
Not only mummies, but many different artifacts are stored in the basement, and never seen by the public, just because the museum is so very crowded. There are wonderful pieces, that any museum in the world would be happy to have that I've seen stored in the gardens!
With the new Egyptian museum out in Giza, much of that which is stored will be put on display. (another reason to take a trip soon!)