Bounded multiplicity branching for symmetric pairs

We prove that any simply connected non-compact semisimple Lie group $G$ admits an infinite-dimensional irreducible representation $\mathrm{\Pi }$ with bounded multiplicity property of the restriction $\mathrm{\Pi }{\mathrm{\mid }}_{G^{\mathrm{\prime }}}$ for all symmetric pairs $(G,G^{\mathrm{\prime }})$. We also discuss which irreducible representations $\mathrm{\Pi }$ satisfy the bounded multiplicity property.