  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
$d<r-1$. Namely, we answer an old question posed by Colli in [Annales de
l'Institut Henri Poincare-Nonlinear Analysis, 15, 539--580 (1998)] on
typicality of the coexistence of infinitely many non-hyperbolic strange
attractors for $3\leq d<r-1$.
