  For an Abelian group $G$, any homomorphism $\mu\colon G\otimes G\rightarrow
G$ is called a \textsf{multiplication} on $G$. The set $\text{Mult}\,G$ of all
multiplications on an Abelian group $G$ itself is an Abelian group with respect
to addition; the group is called the \textsf{multiplication group} of $G$. Let
$\mathcal{A}_0$ be the class of all reduced block-rigid almost completely
decomposable groups of ring type with cyclic regulator quotient. In this paper,
for groups $G\in \mathcal{A}_0$, we describe groups $\text{Mult}\,G$. We prove
that for $G\in \mathcal{A}_0$, the group $\text{Mult}\,G$ also belongs to the
class $\mathcal{A}_0$. For any group $G\in \mathcal{A}_0$, we describe the
rank, the regulator, the regulator index, invariants of near-isomorphism, a
main decomposition, and a standard representation of the group
$\text{Mult}\,G$.
