Cannot rotate a camera on a motion path that is targeted to an empty. I am fairly new to Blender and have run into a problem I cannot seem to overcome. 

I have a camera on a horizontal, semi-circular motion path and it moves nicely around an object. The camera is targeted to an empty inside the object so as the camera moves around the object it continues to point at the empty (and hence the object). 

What I wish to do is to rotate the camera slightly to tilt the view as the camera continues to move along the path. The tilt would be on the axis that does not disrupt the camera pointing to the empty.

The problem is that I cannot rotate the camera. All xyz rotation setting changes have no affect on the camera. Rotating the targeted empty is possible, but does not affect the orientation of the camera.

I suspect targeting to the empty has locked the orientation of the camera and I am not sure how to override this - if even possible?
Based on the description of @batFINGER, I was able to perform the steps to allow for camera rotation during the animation.

Setup:


empty for tracking (target)
empty for camera (dolly)
camera
BezierCircle (path)


Constrains:


for the camera empty:


follow path "BezierCircle" (don't forget to click "animate path")
Track to "empty for tracking" (make sure to set -Z and Y)

for the camera itself


constraint: child of "empty for camera"



This should now have the camera tracking the "empty for tracking"


go to camera view and select your camera: it is still possible to rotate the camera