  Bleher et al. began studying higher codimension Iwasawa theory for classical
Iwasawa modules. Subsequently, Lei and Palvannan studied an analogue for
elliptic curves with supersingular reduction. In this paper, we obtain a vast
generalization of the work of Lei and Palvannan. A key technique is an approach
to the work of Bleher et al. that the author previously proposed. For this
purpose, we also study the structure of $\pm$-norm subgroups and duality
properties of multiply-signed Selmer groups.
