Stevenson played a leading role in several local civic societies (aka civil societies, or groups of community of citizens often linked by collective interests and activities) including serving as the founder and first president of the Equal Franchise Society of Philadelphia, co-founder and two-term president of the Civic Club of Philadelphia (a group of women who advocated for civic reform and improvement), the president of the Acorn Club for 25 years, president of the Contemporary Club, and chair of the French War Relief Committee of the Emergency Aid of Pennsylvania. She also served on the Women's Centennial Committee of the Philadelphia Centennial Exhibition of 1876, which created an exhibition known as the "Women's Building" that showcased "for the first time, at an international exposition, the intimate bonds, shared values, and material achievements of women" and was hailed as a milestone in the women's movement of the 19th century.