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H1B with company not able to do LC

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  • H1B with company not able to do LC

    Hi,
    I came to the US on 2001 with an H1B. I was laid off and I got a new sponsor in January 2004. My H1B is good till October 2006.
    I'd like to file LC and adjustment of status to apply for my GC but I know this company won't be willing to do so.
    What do you suggest I do?
    Is it possible to keep working for my sponsor and find another company willing to apply for the LC and GC? In that case, can I have concurrent H1B sponsors? If so, how does this work?
    Any other options?
    Thanks
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