Morphing fitted item

PerttiA

I have used Blender to make morphs for the base figures, but now I wanted to make morphs that would mostly effect a fitted 'item'.
In DS the base figure is posed and this pose is changing the item, the item also has morphs of it's own that are applied.

What I'm trying to do would be a sort of corrective morph that would partly effect the base figure but mostly the fitted item.

I can OBJ export the base figure and the fitted item separately to Blender, but in there they are separate objects and I don't know how to proceed from there.
I tried parenting, but that moved the item way off the base figure.

Any hints on how to proceed?