Can a cat mix with a dog?

Could you elaborate on the feasibility of a cat coexisting peacefully with a dog within the same household? While we often perceive these two animal species as having contrasting temperaments and behaviors, is there a possibility that they could coexist harmoniously? Could you provide any insights into the challenges that might arise in such a setup, and perhaps some strategies to overcome these challenges and foster a healthy relationship between the two? Furthermore, are there any specific breeds of cats or dogs that are more suited for this kind of coexistence? Thank you for your insights on this intriguing question.