Ithaca Mag 10

[B. Dudley]

The tang screws loosening up can cause an up and down movement in the stock head. Specifically the rear one.
If you find that tightening the screws takes care of it, then you know that is the issue or kind of the issue.
I say kind of because you also have to look at if the screws are correctly timed. Take the rear tang screw for example. Is the end of it finished flush with the upper tang? Or is it sunk down in below the level of the tang. If it is sunk down in, then it is loose for sure. But... If the screw is flush, and tightening it more (so that it sticks up above the tang) also tightens up the stock, then you know the issue is wood related as suggested above.
A way to remedy this situation could be to put some cards rock shims under the trigger plate tang or upper tang at the rear. This will allow you to tighten the screw more for a snug fit, yet not have the screw stick up above the tang.