I know that an i386 Debian can be easily installed using debootstrap on a already installed x86_64 Debian.
But the scenario is an i386 Debian is already installed on a machine that has a x86_64 CPU, and I want to bootstrap a x86_64 Debian on it. Can this be done?
The answer is yes, with a bit more extra work.
First install a x86_64 kernel, so that debootstrap can run x86_64 apps in the chroot. An i386 system can run under a x86_64 kernel, and Debian has prepared everything for you, just:
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Select x86_64 kernel in the grub menu and boot, and the rest is just a normal debootstrap process:
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Exit chroot and add the new entry in grub’s config file, reboot. Now you have a newly installed x86_64 Debian.
For more detail, see this chapter of Debian GNU/Linux Installation Guide and debootstrap manual.