James,
You don't need to use another cue stack to be part of a chase. You can use the in built chase options. {Shift} {Effect} key press will take you to the in built effects part of the desk. Select the channels that you want to be part of the effect and then select what you would like them to do. There are loads of different of colours pans and other effects. If you have also the auto groups and and auto palettes on (from the patch screen) then it will make things obviously easier to select stuff for the chases.
If you then save the cue that you want with the effect running - it's loaded as part of the cue next time.
Ben