By structure, I mean that which is defined here: http://en.wikipedia.org/wiki/Structure_%28mathematical_logic%29
What I'm looking for is a way of gluing together structures so that each structure used is embedded within the whole glued-together object. (Each--meaning not just "most")
I don't need this embedding to be elementary; just something that "preserves" function, relation, and constant symbols.
I would think that some type of product would work.
If we have a set of structures $S$, then I want to show there exists a structure $U$ with the property that there is an injective homomorphism from every structure $A$ in $S$ into $U$.
The following link will help solidify what I mean: http://en.wikipedia.org/wiki/Structure_%28mathematical_logic%29#Homomorphisms_and_embeddings
Are there two cases, depending on the size of $S$, finite and infinite? What I'm hoping for is some type of product of the structures in $S$ where $S$ is going to be a "large" collection of structures.