  We show that the theories of partially ordered sets, lattices, semilattices,
Boolean algebras, Heyting algebras with a further coarser partial order, or a
linearization, or an auxiliary relation have the strong amalgamation property,
Fra\"\i ss\'e limits and, in many cases, an $ \omega$-categorical model
completion with quantifier elimination. The same applies to Kronheimer and
Penrose's causal spaces. On the other hand, Urquhart doubly ordered sets do not
have the amalgamation property.
  Our main tool is the superamalgamation property (the strong amalgamation
property is not enough), thus we provide further arguments suggesting the
usefulness of the superamalgamation property also in pure model theory, not
only in algebraic logic.
