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We know there are small companies on earth like Picard's vineyard and Sisko's (Ben's dad) restaurant, but are there any large private companies that operate within Federation space like say a Procter and Gamble, FedEx, or Boeing size companies?
Private company means private company, not publicly traded stocks, etc. This question has nothing to do with the economic or monitary system or means of exchange. This has to do with any large private company that provides goods or services to others.