Something similar to this, making separate outer and inner pieces.

First an outside piece which will be cut by these planes:



And then discard these areas:



And then a smaller inner piece which will be cut by these planes:



And have these areas discarded:



So now the outside and inside remaining pieces look like this:



You can select these spots and do a Loft to connect them, then Edit > Join the pieces together:



Hope this helps!

- Michael