H4 pending apply for H1B question

I filed status change from H1 to H4 right before my previous H1b was expired because that company can't sponsor my H1b any more. I am now in H4 pending status. Another company gave me an offer and is willing to apply a new H1b for me. Is it possible to apply an H1b while my H4 application is pending? If so, what documents will be required? Thanks in advance for your input.