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We explore how firms grow by adding products. We leverage detailed data from Japan's cotton spinning industry at the turn of the last century to do so. This setting allows us to fully characterize the type of differentiation (vertical or horizontal) of new product introductions as well as whether the product is within or outside of the firm's prior technological capabilities. We find that trying to introduce innovative products beyond the firm's previous technologically feasible set, even if such trials fail, is a key to firm growth. Indeed, it mostly facilitates growth through the firm's later success in horizontal product diversification. In long-term outcomes, the right tail of the firm size distribution becomes dominated by firms that first moved into technologically challenging products and then later applied their newly acquired technical competence to horizontal expansion of their product portfolios. Two mechanisms through which this knowledge transfer occurs are greater production system flexibility and higher product appeal to downstream buyers.