Learn Spanish (Latin America): Mi hermana necesita su vestido.

In Spanish, possessive adjectives like su don't change based on the gender of the owner like they do in English (his vs. her). Su can mean "his," "her," "your," or "their." Instead, they only change to match the number (singular or plural) of the thing being owned.

If multiple sisters shared the dress, would it become sus vestido?

No, it would still be su vestido. This is a common trap for English speakers! Possessive adjectives match the item being owned, not the people who own it. Because there is only one dress (vestido), you use the singular su, no matter how many sisters there are. You only use sus if there are multiple dresses (sus vestidos).

Why does mi not end in an "a" to match the feminine word hermana?

Unlike nuestro (our), the possessive adjectives mi (my), tu (your), and su (his/her/their) do not change for gender. They only change for number by adding an "s" if the thing owned is plural. So it is always mi whether the noun is masculine or feminine!

Why isn't there a "personal a" before su vestido?