This paper reports on new results concerning the combination of non-standard semantics via interpreters. We define what a semantics combination means and identify under which conditions a combination can be realized by programs (robustness, definedness preserving). We develop the underlying mathematical theory and examine the meaning of several non-standard interpreter towers in computational terms. Our theoretical framework explains classical results like interpreter towers and shows that the Futamura projections are a particular instance of a more general principle of semantics modification which applies to all robust semantics. Our results suggest a novel technique for the implementation of programming language dialects by composing a hierarchy of simpler, more elementary non-standard interpreters.