Yes, but it is still up to USCIS to decide whether to extend the status or not.
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You may want to change and extend to a B2 visitor as the B1 is for business meetings. I would urge you to contact an experienced immigration attorney to process this case for you. Also there is no guarantee immigration services will approve your case and you should be aware that it may take 3 months or longer to get a decision so there is a risk that if you get a denial that your time here is counted as out of status. Again consult with an experienced immigration attorney before you file to get the details of your case and get the full picture.
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You probably can ask for a change/extension of status. Meet with an Immigration lawyer in your area to go over your documents and situation.
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