  Algebra objects in $\infty$-categories of spans admit a description in terms
of $2$-Segal objects. We introduce a notion of span between $2$-Segal objects
and extend this correspondence to an equivalence of $\infty$-categories.
Additionally, for every $\infty$-category with finite limits $\mathcal{C}$, we
introduce a notion of a birelative $2$-Segal object in $\mathcal{C}$ and
establish a similar equivalence with the $\infty$-category of bimodule objects
in spans. Examples of these concepts arise from algebraic and hermitian
K-theory through the corresponding Waldhausen $S_{\bullet}$-construction. Apart
from their categorical relevance, these concepts can be used to construct
homotopy coherent representations of Hall algebras.
