Uncountable interval of varieties of involution semigroups sharing a common semigroup variety reduct

A pair of involution semigroups sharing a common semigroup reduct of order eight is constructed with the property that the varieties they generate bound an interval that contains an uncountable chain. Consequently, there exist uncountably many non-finitely generated varieties of involution semigroups sharing a common semigroup variety reduct that is finitely generated.