  Consider the adjoint restriction inequality associated with the hypersurface
$\{ (\tau, \xi) \in \mathbb{R}^{d+1} : \tau = |\xi|^2 \} \cup \{(\tau, \xi) \in
\mathbb{R}^{d+1} : \tau - \tau_0 = |\xi - \xi_0|^2\}$ for any $(\tau_0, \xi_0)
\neq 0$. We prove that extremizers do not exist for this inequality and fully
characterize extremizing sequences in terms of extremizers for the adjoint
restriction inequality for the paraboloid.
