Single Linux install bootable on multiple architectures

So it would be a single installation, sharing user data, config files, programs, etc., but I could take the boot drive and plug it into an x86 machine and it would boot and then later continue my work on an ARM machine and it would boot. This could be implemented, for example, by having multiple copies of every binary, each compiled for different architectures, connected by symlinks. Is this possible? Do any distros do this?