What is a "combo install file"? IIUC, the only way to get a macOS install package is to download it from an Apple server. The Apple server will talk to your Mac, find out what install package it needs and deliver that. There has not been any "fat binary" OS installer for about fifteen years, when MacOS 10.5 Leopard came on a DVD. For Apple to deliver a "combo" install package from its servers would be an enormous waste of resources, since Apple knows what machine it is uploading to.
The main thing that makes your Mac unique is primarily in ~/Library/ (user library directory). That stuff is almost entirely platform-agnostic, so you might be able to do some kind of magic with a symbolic link that points ~/Library/ (or even your entire home directory) to a folder on the external ssd. It is kind of risky, though, because your computer will get confused and misbehave if the external device is not mounted.