You should split complex objects into simpler parts. I mean, don't use one cage for your entire project but use one for each sub part.
Another thing is, that the cage object not always recognize the right patches. You can also use the PatchCreator tool to define single patches, that you can put under a MultiPatch object later.
You can even create patches manually bei selecting the desired splines and call "SplinePatch" (= create a SplinePatch object).