A supersolid combines density order with phase coherence, and doped lattice solids ask whether added defects can become coherent without melting the ordered background. We study a soft-core Bose-Hubbard model with isotropic hopping and an engineered non-axisymmetric dipolar interaction, Vij=V2(xij2−yij2)/rij5+W6/rij6
Nearby in the stack
, where the sign-changing
dx2−y2
component selects a fixed
(q,0)
stripe channel and the
W6/r6
core stabilizes the short-distance attractive branch. Using sign-problem-free quantum Monte Carlo method with worm algorithm, we find that the half-filled stripe parent responds asymmetrically to doping: the hole side forms locked commensurate stripe solids with vanishing superfluid stiffness, whereas the particle side forms a stripe supersolid with finite compressibility
κ>0
, finite superfluid stiffness
ρs>0
, and enhanced double occupancy
D
. Keeping the same off-site kernel while increasing
U/t
toward the hard-core limit shows that the particle-side supersolid disappears once doublon-like defects are projected out. Thus the engineered dipolar kernel selects the fixed
(q,0)
stripe channel, while onsite softness selects the phase-coherent defect sector.