  In this work, as an attempt in understanding the interplay between
deformations of the external and internal spaces associated with the
probe-brane embedding submanifold, we construct the zero-temperature phase
diagram for the coupled phase between two two-dimensional defects stacked
parallel in a four-dimensional ambient spacetime. Different UV parameters are
turned on for different defects. We study the system in the quenched strong
coupling limit, using holography with probe brane approximation, realized
explicitly through the D3/D5 system. This coupled phase is holographic dual to
the presence of spontaneous symmetry breaking of the individual ultraviolet
flavor symmetries associated with the double heterostructure of the defect
layers. We characterize this solution by its infrared geometric data, and
present the numerical result showing a first-order phase transition between the
asymmetrically coupled phase and the more mundane decoupled phase.
