But you can. The H1-B program is designed for all that. The sponsor has to prove they're paying market-ish rate (in practice it's at the low end of market, but close enough). And the employee can quit and go to any company willing to file a little bit of paperwork.
But that's IF you're the kind of worker the H1-B was designed to allow into the USA – someone highly skilled and in demand, with the cultural competence to navigate US society. The hordes of TATA people, I don't know.
The real issue with the H-1B (in my opinion) is that you need to jump to a new employer very quickly if you quit. You can't quit a bad situation and then spend a couple of months trying to get a better one.
But that's IF you're the kind of worker the H1-B was designed to allow into the USA – someone highly skilled and in demand, with the cultural competence to navigate US society. The hordes of TATA people, I don't know.
The real issue with the H-1B (in my opinion) is that you need to jump to a new employer very quickly if you quit. You can't quit a bad situation and then spend a couple of months trying to get a better one.