This situation isn't just hypothetical. In the 1940s the grocery chain A&P was the largest retailer of any sort in the US and there was a real concern that they were anti-competitive because they owned a number of food processing plants in addition to their stores. The Federal government brought suit but didn't succeed in breaking up A&P. Ultimately, of course, A&P didn't succeed in monopolizing groceries, and even went bankrupt a decade or so ago, but they were the WalMart of their time.