stay with current employer

If the working nature at the new firm is extremely similar to your current position, and it's within the same metropolitan area, consider the move.

Otherwise your LCA becomes invalid and you are better off staying with your current employer.

By the way, foreign nationals can have multiple approved H1-Bs. My company (Fortune 500) has gotten H1-Bs for people we want to hire, but they choose not to come. These are foreign nationals who are already under H1-B status for a different company.