  Dielectric metasurfaces supporting quasi-bound states in the continuum
(quasi-BICs) exhibit very high quality factor resonances and electric field
confinement. However, accessing the high-Q end of the quasi-BIC regime usually
requires marginally distorting the metasurface design from a BIC condition,
pushing the needed nanoscale fabrication precision to the limit. This work
introduces a novel concept for generating high-Q quasi-BICs, which strongly
relaxes this requirement by incorporating a relatively large perturbative
element close to high-symmetry points of an undistorted BIC metasurface, acting
as a coupler to the radiation continuum. We validate this approach by adding a
$\sim$100 nm diameter cylinder between two reflection-symmetry points separated
by a 300 nm gap in an elliptical disk metasurface unit cell, using gallium
phosphide as the dielectric. We find that high-Q resonances emerge when the
cylindrical coupler is placed at any position between such symmetry points. We
further explore this metasurface's second harmonic generation capability in the
optical range. Displacing the coupler as much as a full diameter from a BIC
condition produces record-breaking normalized conversion efficiencies >10$^{2}$
W$^{-1}$. The strategy of enclosing a disruptive element between multiple
high-symmetry points in a BIC metasurface could be applied to construct robust
high-Q quasi-BICs in many geometrical designs.
