In the US a company may have employees each in different unions.

Consider a Hollywood movie studio, where the writers, actors, stage workers, and truckers may all be in different unions.

The US unions are by trade, and I think that's what l3uwin also means for NL.

That said, multi-unionism is indeed more common in Europe, if my reading of Google Scholar is correct. Eg, "Multi-unionism and the Representation of Sectional Interests in British Workplaces" at https://journals.sagepub.com/doi/pdf/10.1177/104346311454631...

> Unlike in the United States, exclusive jurisdiction is exceptional in Europe (Visser, 1992), and unions commonly negotiate with employers simultaneously with other unions on the level of the sector as well as at the company level (Akkerman, 2008). The majority of the European Union member states have multiple labor union confederations, organizing members along political, religious, or occupational (status) lines (Eurofound, 2014). Even in the United Kingdom, Austria, Ireland, and Latvia— countries with just one union confederation—unaffiliated unions and union representation by several unions within the same confederation exist. Thus, multi-union bargaining is a common if not dominant feature of Western European industrial relations. Sometimes, these unions coordinate their bargaining activities, for instance, by setting joint wage demands and synchronizing the communication to their rank and file. Joining forces increases their bargaining power.