My mother loves tulips. So does my older sister.

Literal

Mother [topic-は] tulip [possessive-の] flowers [subject-が] greatly-likes-[polite-です]. Older-sister [topic-も] also so-[polite-です]

姉もまたそうです = 'my older sister also (is) so.' も marks the sister as sharing the same quality. またそうです is a concise way to extend a predicate to another subject without repeating it.