I think I know what you mean. You can copy (Ctrl+C) the arc you've drawn, then open the component you want to edit and choose Paste in Place from the Edit menu. Unwanted part of the arc and do your Push/Pull or whatever.
Open the next component for editing and repeat the paste in place thing. Continue until you've edited all of the components.
The point of making components is to keep discreet parts separated. That does mean, though, that geometry drawn outside the component's "wrapper" won't affect the geometry inside.
If you need an illustration, let me know and I'll draw up a quickie.