A framework for composition synthesis is provided in which metalanguage combinators are supported and the execution of synthesized programs can be staged into composition-time code generation (stage 1) and run-time execution (stage 2). By extending composition synthesis to encompass both object language (L1) and metalanguage (L2) combinators, composition synthesis becomes a powerful and flexible framework for the generation of L1-program compositions. A system of modal intersection types is introduced into a combinatory composition language to control the distinction between L1- and L2-combinators at the type level, thereby exposing the language distinction to composition synthesis. We provide a theory of correctness of the framework which ensures that generated compositions of component implementations are well typed and that their execution can be staged such that all metalanguage combinators can be computed away completely at stage 1, leaving only well typed L1-code for execution at stage 2. Our framework has been implemented, and we report on experiments.