Definitions for "INTERSTAGE"
Fujitsu's broad family of modular, flexible software products that allows enterprises to design, develop, deploy, and manage scalable, customized mission-critical applications securely and reliably. INTERSTAGE site
In a two stage compressor system, this is the cross over piping on top of the compressor that connects the low side to the high side. One could also think of it as low side, intermediate, and high side.
This provides the mechanical interface between two launcher stages and also hosts the separation device, the thrust vector control electrical unit and the batteries