Introducing a new cat to a household can initially disrupt the dynamics and may increase play fighting behaviors among existing cats as they establish their social hierarchy. This adjustment period can lead to more frequent and intense play sessions as cats test boundaries and assert dominance or establish roles. It's important to monitor these interactions to ensure they remain playful and do not escalate into aggression. Gradual introduction and providing separate resources can help minimize stress and facilitate a smoother integration into the group dynamic.