Yes. As one example, Oreos are an imitation of the Hydrox cookie. You could also look at something like Coca-Cola and Pepsi-Cola. Coke is still more popular than Pepsi, but Pepsi took a lot of market share that might otherwise have belonged to Coke.

As another example, in Australia, Vegemite, a food spread based on an extract of brewers yeast, was designed as a competitor/replacement as a result of shortages of Marmite, a British made spread, in the 1920s. It now has much greater market share in Australia, being considered an essential in most families, although it has low market share elsewhere.