  We relativise double categories of relations to stable orthogonal
factorisation systems. Furthermore, we present the characterisation of the
relative double categories of relations in two ways. The first utilises a
generalised comprehension scheme, and the second focuses on a specific class of
vertical arrows defined solely double-categorically. We organise diverse
classes of double categories of relations and correlate them with significant
classes of factorisation systems. Our framework embraces double categories of
spans and double categories of relations on regular categories, which we
meticulously compare to existing work on the characterisations of bicategories
and double categories of spans and relations.
