You can’t necessarily have both Roblox and your camera script running at the same time, however, you could mimic Roblox’s camera script by either copying the Roblox camera scripts and putting them in StarterPlayerScripts, and editing those files’ code, which overrides the base code, or you can make a new camera script, which may be easier as you wouldn’t need to understand Roblox’s code.
To make your own code you could make a client script, that gets RunService which has the function RenderStep. Then you can have a function that sets the CFrame of the Camera to the CFrame of the Player’s Head, and then when the mouse moves, the character faces a new direction based of the mouse movement. We can achieve this with UserInputService. First, we lock the mouse with MouseBehavior property, and then use GetMouseDelta (The page also has a Camera script example), which gets mouse movement when the mouse is locked. And lastly, we can also achieve leaning or shaking by just editing the camera CFrame slightly.