I am a researcher on a J1 visa for a given academic institute. I have applied for a grant with another academic institute and if I get the funding I will be able to work remotely with that institute. My question is this: How can I "work" both jobs without doing anything illegal? Can I ask my current employer to allow me to work extra hours with the other employer? Or is there a limit to maximum number of hours/week that a J1 visa holder is allowed to work? If this is possible what will my current employer need to do? Will I have to apply for another DS-2019?