Is it possible to make the box between ribcage and pelvis twist and bend? I’ve messed around with the armature a bit but couldn’t really find a way to make it work.
I want it to move when I move the ribcage box or pelvis box.
The selected box is the one I want to bend and twist when I pose my mannequin in pose mode.
Welcome 
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When the object to one then usually this is done by weight paiting and you get:
BendingMiddlePart.blend (111.8 KB)
I haven’t using a rig for multiple objects yet but i guess parenting all objects to the rig… well i try… and with a subdivided cylinder… :
Thanks to you i have learnt something today 
And (edit): @digitvisions seems to have added an image while i was typing… 
Since the armature hierachy is folded we can say that everything else is not rigged (because does not have armature as parent). Other than this we can’t say much about with your image.
You need to watch weight painting tutorials like this one: https://www.youtube.com/watch?v=SCWZr-It1bE
The loop lines are what divides the object to allow for bending.
Constraints are not relevant here.
I originaly wanted to highlight that what you are showing does not matter too much according to your initial question and secondly was talking about what we actually can see or can not see. So in in this regard i meant the child-parent-relationship like so :
What you showed is not an actual an answer to the question @digitvisions made to help you better.
Also:
Did you had a look into my examples (and blend file) the first is doing a simple distorted bending and the example with the cylinder (more subdivided) is doing more what one my call bending…
Or:
Yyou may simply have to look into some rigging/skinning tutorials ? Like for example starting with Docs-Blender Manual: Animation → Armatures → Skinning … 
Oh… the auto weight feature almost had done this…
weight painting just is to refine this and you also can set the weight “directly” :
