  Let $R$ be a commutative Noetherian local ring. Assume that $R$ has a pair
$\{x,y\}$ of exact zerodivisors such that $\dim R/(x,y)\ge2$ and all totally
reflexive $R/(x)$-modules are free. We show that the first and second
Brauer--Thrall type theorems hold for the category of totally reflexive
$R$-modules. More precisely, we prove that, for infinitely many integers $n$,
there exists an indecomposable totally reflexive $R$-module of multiplicity
$n$. Moreover, if the residue field of $R$ is infinite, we prove that there
exist infinitely many isomorphism classes of indecomposable totally reflexive
$R$-modules of multiplicity $n$.
