  We demonstrate the existence of $N$-tuple critical points of uncharged AdS
black holes in generalized quasi-topological theories. The criticality is shown
to have a geometrical interpretation described by the Maxwell's equal area
rule. We present a compact reformulation of the area rule and identify a
criterion for the emergence such points. Using this criterion, we construct
several multi-critical points with genuine generalized quasi-topological
densities, including a quadruple and a quintuple points.
