First, consider a (co)bordism category with multiple ceilings and floors with interpenetration. (I could have done three, but I didn’t really want to argue with inkscape this morning)
Or consider a swiss-cheesed pair of pants:
One is tempted to think about wild/fractal (co)-bordism categories: a pair of pants, swiss-cheesed by a pair of pants, swiss-cheesed by another pair of pants, and so on and so forth.
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Klein pants!