  We present a new Clash-of-Symmetries mechanism in the context of an
intersecting domain-wall brane model in 5+1-dimensional Minkowskian spacetime
recently proposed by the authors. This new application of the Dvali-Shifman
idea is designed for localizing gauge fields on a domain-wall intersection and
we employ it by adding a gauge group $G$ and giving the scalar fields which
form lump-like profiles gauge charges. These fields in turn break $G$ to two
different subgroups $H_{1}$ and $H_{2}$ on each domain wall, and the gauge
fields of these subgroups are taken to be localized to the respective walls by
the confinement dynamics of $G$. There is then a further breaking on the
domain-wall intersection to $H_{1}\cap{}H_{2}$ and gauge fields of this overlap
group can then be localized to the intersection if they belong inside
non-Abelian subgroups of both $H_{1}$ and $H_{2}$ which are spontaneously
broken on the intersection and confining in the 4+1D bulks of the respective
domain-wall branes. This mechanism has some similarities to the
Clash-of-Symmetries mechanism on a single domain wall except that in this case
$H_{1}$ and $H_{2}$ need not be isomorphic. We then give some interesting
examples of the mechanism in an SU(7) gauge theory, several of which result in
the localization of the Standard Model gauge group.
