Is a garden shed a possibility?
If there is garden space, and parental permission, a shed could hold a lot of packed stuff, freeing up room space for displays. Probably not blue boxes, for fear of damp, but fortunately Playmobil itself if almost 100% cold and damp proof.
I used to have a lot stored in the attic, but it was too awkward to get it down to view so it just piled up in secret.