When you purchase an annual family plus membership as a gift, can you stipulate the start date of that gift membership?

Yes

If you'd like to purchase a membership for another person, purchase a gift certificate in the amount of the membership. This way, they will be able to choose the start date. If you purchase a "gift membership" the membership begins on the date of the purchase. Please visit this page to purchase the gift certificate: https://www.mychildsmuseum.org/visit/gift-certificates