Is it possible? If so how?
Definitely possible, but you’ll likely have to get some supplies that people don’t typically have laying around the house. You could just use a stainless steel polishing cloth (I recommend Cape Cod) and that’ll brighten up the shine quite a bit, you’ll still likely see some of the machined finish (just shinier). To go all out with it and get a mirror shine, you’ll need several grades of sandpaper, a machine to turn the cups (a lathe or even a drill if you’re careful), and some rouge (polishing compound). This route might end up affecting the play too.
Same concept as for aluminum but will likely take a little more work
I’ve polished mine! Works well with a lathe and sandpaper from 1000 to 2500 grit as well as polishing compound.
Do you have a picture?
Some of the dremel tool clone (not a real dremel brand) sets have polishing compound in them for cheap (>$10). Don’t use a grade lower than a polishing grit at 1st as you can remove enough metal to alter play. Plus the flea won’t need a high grit polish 1st, it’s machined fine enough as is.