From the Super Mario Wiki
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Clothing are items in the Mario & Luigi series that serve much like Armor in Super Mario RPG: Legend of the Seven Stars. Clothing mainly exists to boost defense power, but some clothes boost other stats such as speed, attack, and others as well. The first two games in the series have overalls as clothing, but Mario & Luigi: Bowser's Inside Story features an expanded set of clothing that also includes gloves, socks, and boots for Mario and Luigi and shells, arm bands, rings, and fangs for Bowser. Mario & Luigi: Dream Team further expands on this by adding hammer as a type of wear.
Clothing are found usually in various specialty shops, but defeated enemies can sometimes drop clothing.