  We consider the situation in which some class of structures has the Strong
Amalgamation Property (SAP) with the further requirement that the amalgamating
structure can be taken over the set theoretical union of (the images of) the
domains of the structures to be amalgamated. We call this property SAPU.
  The main advantage of SAPU over SAP is that there are many preservation
theorems showing that we can merge different theories with SAPU still obtaining
a theory with SAPU, hence with SAP. In particular, we elaborate on some
classical results by R. Fra\"iss\'e and B. J\'onsson, showing that the class of
partially ordered sets with a family of operators has SAPU. More generally, the
argument applies to various theories with possibly many binary relations and
unary operations together, possibly satisfying some coarseness, isotonicity and
closure conditions.
