  We introduce the notion of \pi-extension of the semigroup \mathbb{Z}_+ and
study the extensions of the Toeplitz algebras by isometric operators. We show
that when the action of the Toeplitz algebra is irreducible all such extensions
generate the same algebra, i.e. there are no non-trivial extensions of the
Toeplitz algebra. Also we provide the examples of the non-trivial extensions of
the Toeplitz algebra in case its representation is reducible.
