You can always file another H-1. You can file for an H-1 renewal, you can file for an H-1 transfer, you can file for an H-1B amendment even if the H-1B is denied. While in the USA depends upon whether or not you have status. If you are maintaining status you can file for an extension and another amendment because one denial does not foreclose another application under the same category.
But if you are not in status chances are you will have to go outside the USA for visa stamping before you can start working with a new approval, but a new application can always be filed. More...
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