J1 Transfer over a "middle" institute

Hello researchers!
Currently I hold a J1 Visa valid for two years without the need to go to my country of origin when it ends. My status is the following: for the second year I do not want to continue with my current university who sponsors my VISA. My question is the following: Can I agree with a new INstitute, which will ask to transfer my VISA, then when the transfer happens to have an offer by a research lab of a company and transfer my VISA again from the middle institute without even having started there and informed them in advance? What problems can be created?
Currently I hold a J1 Visa valid for two years without the need to go to my country of origin when it ends. My status is the following: for the second year I do not want to continue with my current university who sponsors my VISA. My question is the following: Can I agree with a new INstitute, which will ask to transfer my VISA, then when the transfer happens to have an offer by a research lab of a company and transfer my VISA again from the middle institute without even having started there and informed them in advance? What problems can be created?