Nowadays bimetallic nanoparticles (NPs) have emerged as key materials for important modern applications in nanoplasmonics, catalysis, biodiagnostics, and nanomagnetics. Consequently the control of bimetallic structural motifs with specific shapes provides increasing functionality and selectivity for related applications. However, producing bimetallic NPs with well controlled structural motifs still remains a formidable challenge. Hence, we present here a general methodology for gas phase synthesis of bimetallic NPs with distinctively different structural motifs ranging at a single particle level from a fully mixed alloy to core-shell, to onion (multi-shell), and finally to a Janus/dumbbell, with the same overall particle composition. These concepts are illustrated for Mo-Cu NPs, where the precise control of the bimetallic NPs with various degrees of chemical ordering, including different shapes from spherical to cube, is achieved by tailoring the energy and thermal environment that the NPs experience during their production. The initial state of NP growth, either in the liquid or in the solid state phase, has important implications for the different structural motifs and shapes of synthesized NPs. Finally we demonstrate that we are able to tune the alloying regime, for the otherwise bulk immiscible Mo-Cu, by achieving an increase of the critical size, below which alloying occurs, closely up to an order of magnitude. It is discovered that the critical size of the NP alloy is not only affected by controlled tuning of the alloying temperature but also by the particle shape.