Does Kotlin Multiplatform have a way to share code between multiple Platform modules (eg linuxX64, linuxARMV7) where the OS (eg Linux) is the same?

yes you can create shared source sets that top level source sets depend on much like common is a predefined source set for all targets

Small Tip: Don't be fooled by the IDE saying no. It will build just fine. There are workarounds to make the IDE happy.

see this: https://medium.com/vmware-end-user-computing/building-an-ios-fat-framework-for-a-kotlin-multiplatform-project-4f2e0b5de2aa

We are working on proper support for the IDE that requires no workarounds and reusing declarations from a library’s shared platform-specific source set of this kind. Stay tuned!

Woo! \o/

If i'm reading this correctly there is a single source set used (part of a Platform module) that the other source sets (part of Platform modules) depend on for shared platform logic. This doesn't sound logical from the onset.