One idea could be exploring the backstory of the cat form more deeply. Maybe the cat has some special powers in that form that are not fully revealed in the original work.
First, study the characters from the original work. Notice their traits, like how the main character is brave yet a bit impulsive. Then, for new characters, give them distinct personalities. For example, if you create a new cat character, make it either very shy or overly confident.
Well, chapter 1 of A Whisker Away manga could potentially lay the foundation for the story. It might give us a glimpse into the world and characters, and perhaps start building the central conflict or theme.