Eliminating certain lines when outlining paths and arrowheads...

hi community...Does anyone know how to outline paths in such a way that outlines the entire outside of the group? In my outlined group below, you can see that the individual paths and arrowheads are each outlined separately. How to I outline the whole organism, so to speak, so that the intersecting parts are not outlined? I tried grouping each line and then nesting those groups under one big group of the whole. I also just tried simply grouping all the components with no nested groups. Thanks!