  In the parlance of relational structures, the Finite Ramsey Theorem states
that the class of all finite chains has the Ramsey property. A classical result
of J. Ne\v{s}et\v{r}il and V. R\"{o}dl claims that the class of all finite
posets with a linear extension has the Ramsey property. In 2010 M. Soki\'{c}
proved that the class of all finite structures consisting of several linear
orders has the Ramsey property. This was followed by a 2017 result of S.
Solecki and M. Zhao that the class of all finite posets with several linear
extensions has the Ramsey property. Using the categorical reinterpretation of
the Ramsey property in this paper we prove a common generalization of all these
results. We consider multiposets to be structures consisting of several partial
orders and several linear orders. We allow partial orders to extend each other
in an arbitrary but fixed way, and require that every partial order is extended
by at least one of the linear orders. We then show that the class of all finite
multiposets conforming to a fixed template has the Ramsey property.
