A few years ago my partner bought me a comercial corset, my first 'real' corset at the time. It doesn't fit me very well, as can be imagined, and I was thinking of taking it apart and trying to make it fit a bit better, replacing plastic bones with steel, etc.
It is single layer with external boning channels, and all the edges I can see are only overlocked.
Has anyone else ever tried this? Any tips?

It's certainly possible. But if you're going to put that much effort in to it, why not make a whole new one? You could figure out what needs changing in terms of fit, take it apart, make a pattern off it, and work from there. Odds are good if they used plastic boning, the fabric isn't terribly high quality.

I have done it once, mine was also a commercial "Burleska" corset, with internal bone casings, double layer, one layer of PVC and one layer of twill. I haven't replaced the bones just took some material to make it tighter on the back panels. I wear it like a bodice (not a corset),
I'm note sure what is the quality of the fabric used for your (single layer) corset, and how much it will last if you decide to modify it. If you modify the pattern to reduce your waist you can end up with fabric torn up and bones peaking out the channels. It would be great to add another layer of a fabric and a waist tape, but it is easier to make the whole new corset than modify this