We report on the effect of in-plane magnetic field $B_parallel$ on stripe phases in higher ($N=2,3$) Landau levels of a high-mobility 2D electron gas. In accord with previous studies, we find that a modest $B_parallel$ applied parallel to the native stripes aligns them perpendicular to it. However, upon further increase of $B_parallel$, stripes are reoriented back to their native direction. Remarkably, applying $B_parallel$ perpendicular to the native stripes also aligns stripes parallel to it. Thus, regardless of the initial orientation of stripes with respect to $B_parallel$, stripes are ultimately aligned emph{parallel} to $B_parallel$. These findings provide evidence for a $B_parallel$-induced symmetry breaking mechanism which challenge current understanding of the role of $B_parallel$ and should be taken into account when determining the strength of the native symmetry breaking potential. Finally, our results might indicate nontrivial coupling between the native and external symmetry breaking fields, which has not yet been theoretically considered.
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