Doesn't multiple lock support then not make it a mutex anymore? I thought that becomes a monitor lock instead? I forget how standardized the terminology is though, there may be leeway in the mutex definition already.

Don't address introduce ambiguous locking order across attempts?

While not obviously problematic, that seems weird enough you would need to validate that it is explicitly safe.

What about mutexes living in shared memory, and each process having a different address mapping?