One thing to consider (if money is no problem) is adding an step-up DC-DC converter. IDK what your current needs to be, but a lot of ATX PSU's these days only make the 12V output from the main SMPS, and then have other buck-type stages for 12V to 5 and 3V3. So if the the parts where choosen correctly, or the correct addon PSU was added, it should be easy to get 19V and whatever current (within power limits/etc).
As for doing it by modding the original, yeah IDK what the max output voltage might be. The main coupled inductor/transformer has some turns ratio, raising the input voltage to that from say 340VDC, gets into pretty dangerous levels, for me anyways, and then some parts like caps would need higher voltage ratings, etc.
Whatever was done, all the over/under protection circuits would have to be altered, and the feedback loops, and more than I can probably imagine to get it to work right.
Personally IDK enough yet do make any big changes to ATX PSU's, but I have a box of them, some I fixed, some I'll look at again soon. But they are too old to sell, they are just for fun and backup's, although IDK how much I trust any of them.