No.
Generally, there will only be one union available to an employee for a specific job. If there were multiple different unions all covering the job, that would dilute the power of a Union. For example, There is no auto workers union competing with the UAW. If there was, both unions would be weaker, and it would be easier for corporations to pit them against each other.
Now, depending on the state you’re in and what kind of “shop” your workplace is, you might have the option of leaving the Union while keeping your current job.
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