If you're looking for anime similar to She and Her Cat, you might like these titles.
What's Michael? Michael is a cat. A cat that is inexplicably attracted to the smell of raw fish, yet horribly repulsed by the smell of toothpaste. A cat that, in a dogfight with a fly, will strafe his master in her sleep. In short, Michael is a cat like any other cat.
The manga centers on a woman who is getting on in years, but all her cats think she's a man so they call her Ojii-chan. One day a brazen cat named Tsushima appears in Ojii-chan's yard.
This story follows the daily lives of a cat named Tama and his cat and dog friends. As their curiosity gets the best of them, they learn enduring values of friendship and teamwork.