I often have this issue too. It’s usually only solved by taking up the shoulders (on a sleeveless garment) because I’m quite short in the torso and not only are the armholes deep, but the overall length of the top is often too long (a hint is if there are darts and they sit below the bust line).
I have also solved this problem — if the overall fit in the top is a bit roomy — by having the sides taken in, and closing up some of the bottom of the armhole in the process. This isn’t always doable but I do have a dress from a year ago that my tailor altered this way successfully. It has a collar so a simple taking up in the shoulders would have been too complicated.
A nice bralette can help if you just want coverage but don’t mind it being open under the arms — I have a rather big bust and I’m not young, so for me, a really wide open armhole that flashes more than a tiny bit of bra is a hard pass.