I agree with Bob O, that a remix can be risky.
"over-mixed" is an interesting term, somewhat akin to "over-produced", where most of the life if gone... too slick and predictable.
Sometimes that rough mix has just the right amount of raw energy, mistakes and all, to make it stand out.
On a remix, the engineer has to get it at least as good as the original mix, which is not always that easy, unless of course they're mixing entirely "inside the DAW box".
I generally would not request a remix, unless, the instrument and/or vocal balance is totally way out of proportion, or has major phase problems, or audible distortion, or other major screw-ups.
There are a lot of problems that can be fixed in mastering, or at least made more tolerable.