Context-dependency of mammalian transcriptional elements has hindered the quantitative investigation of multigene expression stoichiometry and its biological functions. Here, we describe a host- and local DNA context-independent transcription system to gradually fine-tune single and multiple gene expression with predictable stoichiometries. The mammalian transcription system is composed of a library of modular and programmable promoters from bacteriophage and its cognate RNA polymerase (RNAP) fused to a capping enzyme. The relative expression of single genes is quantitatively determined by the relative binding affinity of the RNAP to the promoters, while multigene expression stoichiometry is predicted by a simple biochemical model with resource competition. We use these programmable and modular promoters to predictably tune the expression of three components of an influenza A virus-like particle (VLP). Optimized stoichiometry leads to a 2-fold yield of intact VLP complexes. The host-independent orthogonal transcription system provides a platform for dose-dependent control of multiple protein expression which may be applied for advanced vaccine engineering, cell-fate programming and other therapeutic applications.