Sometimes it is a good idea to put empties inbetween your object's relations. In this case the empty follows the path ('Path' constraint) and the camera is connected to the empty with a 'child Of' constraint. You do that with every path you want to use. The advantage is that you can see all path animations simultaneously without the need for the camera to switch.
Second advantage is that the empties can keep their own 'Track To' constraints, so you don't have to switch several sets of constraints on and off simultaneously!
It might be more convenient to switch the whole 'Child Of' constraint by animating the eye instead of the influence. Just hover over the eye after you switch it on or off and hit I.