  We prove that an infinite (bounded) involution lattice and even
pseudo--Kleene algebra can have any number of congruences between $2$ and its
number of elements or equalling its number of subsets, regardless of whether it
has as many ideals as elements or as many ideals as subsets; consequently, the
same holds for antiortholattices. Under the Generalized Continuum Hypothesis,
this means that an infinite (bounded) involution lattice, pseudo--Kleene
algebra or antiortholattice can have any number of congruences between $2$ and
its number of subsets, regardless of its number of ideals.
