  We prove that the coexistence of infinitely many prevalent H\'enon-like
phenomena is Kolmogorov typical in sectional dissipative $C^{d,r}$-Berger
domains of parameter families of diffeomorphisms of dimension $m\geq 3$ for
$d<r-1$. In particular, we get the coexistence infinitely many non-hyperbolic
strange attractors for $3\leq d<r-1$.
