  Let $(M,g)$ be a compact smooth connected Riemannian manifold (without
boundary) of dimension $N\ge7$. Assume $M$ is symmetric with respect to a point
$\xi_0$ with non-vanishing Weyl's tensor. We consider the linear perturbation
of the Yamabe problem $$(P_\epsilon)\qquad-\mathcal L_g u+\epsilon
u=u^{N+2\over N-2}\ \hbox{in}\ (M,g) .$$ We prove that for any $k\in \mathbb
N$, there exists $\epsilon_k>0$ such that for all $\epsilon\in (0, \epsilon_k)$
the problem $(P_\epsilon)$ has a symmetric solution $u_\epsilon ,$ which looks
like the superposition of $k$ positive bubbles centered at the point $\xi_0$ as
$\epsilon\to 0$. In particular, $\xi_0$ is a {\em towering} blow-up point.
