You need to keep playing and levelling up to unlock more slots to send more cats. I hope I’m understanding your question correctly!

CHeck out the stage hint and collect as many of the recommended items as possible (espy the dress and shoes as this give the highest bonus) it will also help if you can collect more than the recommended clothes in the same set. You can also level up your relics (can’t remember which one is best for that round) to give you a higher bonus as well. Hope this helps!

Have you checked your mail under letters? That’s where you can collect blueprints once you have reached the proper level with the character. You only get blueprints at certain goodwill levels.