How to clean oxidized stainless steel Espresso maker?
Whether you have the silver/chrome base or the stainless steel, then unfortunately, no. The steel has lost it's temper (metallurgical changes) and it is not stainless anymore (it can rust now), and this aspect can't be cleaned or repaired. It could be refinished by electroplating it (not really a DIY thing, and although there are electroplaters for hire, the price would be hundreds of dollars). 

On the other hand, I might suggest using a high temperature paint/enamel. The silver (spray) paints just don't make a good chrome finish (so I wouldn't suggest that); but other colors could work. You should not use paint on the inside of the coffee maker, and some of the high temperature paints (like manifold paint) need to be cooked for it to cure. So you should disassemble the coffee maker (remove any plastic) before painting and baking it.

If you decide to paint it, read (especially on the paint can) about surface preparations.