Alberto Alessi is the third generation to lead his family’s iconic design firm. Founded and still based in Crusinallo, about an hour north of Milan, Italy, the firm remains privately owned. In Alessi’s view, both the ownership structure and the location of his company have imbued it with a strong tradition of artisanship—and given its designers the freedom to create as they see fit.

Together, those traits have allowed Alessi to produce some of the most popular houseware designs of the past few decades, as well as some of the most exclusive and sought-after ones. The firm is perhaps best known for its invention of the first home espresso maker, as well as for a certain sense of humor with which it approaches the design of common kitchen utensils.

Nearly 30 years ago, Alessi began shifting away from in-house design and became one of the pioneers of open innovation. Today the firm has relationships with some 200 external designers, many of whom are much better known for expertise in fields such as architecture than in houseware design. A tea kettle by Frank Gehry and a vase by Zaha Hadid are just two products of those relationships.

Alessi met with McKinsey’s...