  A Heyting algebra is supplemented if each element $a$ has a dual
pseudo-complement $a^+$, and a Heyting algebra is centrally supplement if it is
supplemented and each supplement is central. We show that each Heyting algebra
has a centrally supplemented extension in the same variety of Heyting algebras
as the original. We use this tool to investigate a new type of completion of
Heyting algebras arising in the context of algebraic proof theory, the
so-called hyper-MacNeille completion. We show that the hyper-MacNeille
completion of a Heyting algebra is the MacNeille completion of its centrally
supplemented extension. This provides an algebraic description of the
hyper-MacNeille completion of a Heyting algebra, allows development of further
properties of the hyper-MacNeille completion, and provides new examples of
varieties of Heyting algebras that are closed under hyper-MacNeille
completions. In particular, connections between the centrally supplemented
extension and Boolean products allow us to show that any finitely generated
variety of Heyting algebras is closed under hyper-MacNeille completions.
