Temporary extra solo staff

Hmm...

You wrote:
...but hiding empty staves doesn't work for me as I don't want to hide them.

So you want to show them?

Then you wrote:
I don't want to have the empty solo staff the 4/5ths of the score.

OK, so hide them.

See:
https://musescore.org/en/handbook/3/layout-and-formatting#style-score

The idea is to hide the staves where the soloist is not playing and to show the staves that are played.
The staves that are played will print (because they are not hidden). The empty 4/5ths of the score won't print (because they are hidden).

Indeed, what you are saying doesn't seem to make sense - based on what you say you are want, you absolutely do want to hide the solo staff on the systems where the staff is empty, showing it only on the systems where it is not empty. That's precisely what the option to hide empty staves does.

Now, it's possible you don't want to hide other staves when empty. If so, don't enable the global style option for the whole score. Instead, simply set "Hide when empty" in Staff/Part Properties for this staff to "Always".

If you continue to have trouble, please attach your score so we can understand and assist bette.r But based on what you are saying, this is exactly what you want.