  Let $T$ be a complete local (Noetherian) ring. For each $i \in \mathbb{N}$,
let $C_i$ be a nonempty countable set of nonmaximal pairwise incomparable prime
ideals of $T$, and suppose that if $i \neq j$, then either $C_i = C_j$ or no
element of $C_i$ is contained in an element of $C_j$. We provide necessary and
sufficient conditions for $T$ to be the completion of a local integral domain
$A$ satisfying the condition that, for all $i \in \mathbb{N}$, there is a
nonzero prime element $p_i$ of $A$, such that $C_i$ is exactly the set of
maximal elements of the formal fiber of $A$ at $p_iA$. We then prove related
results where the domain $A$ is required to be countable and/or excellent.
