If you're looking for anime similar to With a Dog AND a Cat, Every Day is Fun, you might like these titles.
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.
The daily life of a household that has two cats: Azuki and Daizu. Azuki and Daizu belong to an office worker in her 30s who loves cats. The owner lives with her father, mother, grandfather, and older brother, the latter of whom the cats call "Megane" (Glasses). Megane adopted a Shiba Inu dog named Mamenosuke after Mamenosuke's owner died. Mamenosuke grew up around cats so he actually thinks of himself as a cat.