Punctuation mark before a closing quote mark (Children's picture book)
James once asked the cat, “Have you seen another person like me?”
The cat crossed his legs and thought for a while, then replied, “I’ve scratched lots of trees, but I’ve never seen a boy like you.”
The above would follow the rule you cited. No addition period is needed after the question mark closing the first quote.
Additionally, it follows the rule that there is at most one speaker per paragraph.