i don't know about the 'unite' function.
in illy it's copy>paste in front or back. make sure you create another layer. once you have copied the part of the design necessary for the underbase, lock off all layers except the new one and select that layer and paste. if you want to delete a stroke that you have turned into an object by object>path>outline stroke you have to make sure that object path is situated above the other object. then select the outline path and shift click on the other object to selct both and they click on minus front. make sure everything is ungrouped or it will minus out areas you don't want it to.
you could also (after outlining stroke) go to wireframe view and use the direct selection tool and just click on the outer lines and delete OR you can click on the original stoke of the original object and go to object>path>offset path and type in a negative number (-.025 for instance) then go to wire frame and delete the outer line like above.
in illy it's copy>paste in front or back. make sure you create another layer. once you have copied the part of the design necessary for the underbase, lock off all layers except the new one and select that layer and paste. if you want to delete a stroke that you have turned into an object by object>path>outline stroke you have to make sure that object path is situated above the other object. then select the outline path and shift click on the other object to selct both and they click on minus front. make sure everything is ungrouped or it will minus out areas you don't want it to.
you could also (after outlining stroke) go to wireframe view and use the direct selection tool and just click on the outer lines and delete OR you can click on the original stoke of the original object and go to object>path>offset path and type in a negative number (-.025 for instance) then go to wire frame and delete the outer line like above.