Most Stainless frames are a martensitic stainless and will attract a magnet. I also suspect 416
This is from the AWS (American welding society) web site
Type 416 Martensitic stainless steel is a free-machining grade that is weldable providing the process, or filler metal, does not supply hydrogen that can react with the sulfur or selenium in the base metal to produce porosity. Due to the amount of sulfur that enters the weld due to dilution, the filler metal selection should provide weld metal that can tolerate these elements without hot cracking. An E312 series stainless steel is one of the better choices. A nickel-alloy filler metal cannot be used due to the formation of low melting nickel eutectics, which cause hot cracking. Personally, I would recommend the 312 series over the 420 or the 309.
I am a serious metal guy, a pipe fitter fair stick welder, I have a brother that is a certified welding inspector, have friends that are great welders and I think welding a steel (but never aluminum) frame back together successfully could be done. Be very difficult to keep it perfectly aligned due to weld distortion and weld shrink. Plus, then you would need to remachine the interior surfaces and clean up the outside ones.Be a labor of love because even at $15 an hour your going to have way more time in it than its worth. Frames are not that hard to come by.