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You can have many H1s at the same time, but you must have applied for and
received acceptance for each H1 before beginning employment.
INS FAQ says:
"Who can an H-1B alien work for?
H-1B aliens may only work for the petitioning U.S. employer and only in the
H-1B activities described in the petition. The petitioning U.S. employer may
place the H-1B worker on the worksite of another employer if all applicable
rules (e.g., Department of Labor rules) are followed. H-1B aliens may work for
more than one U.S. employer, but must have an I-129 petition filed by each
employer."
I\'m not an attorney.