CentOS

What if anything could go wrong when this is done?

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Do not do this on a system with precious contents. Test this on a VM of no importance to anyone.
May have unknown consequences and could cause losses.
COMPLETELY AT-YOUR-OWN-RISK. NO WARANTIES EXPRESSED OR IMPLIED. YOU HAVE BEEN WARNED.

Start with a i686 (32-bit) CentOS installation.

Fetch the kernel from a mirror using wget http://centos.some-mirror.org/.../kernel-2.6.32-{some-version}.el6.x86_64.rpm
rpm -Uhv --force --ignorearch kernel-2.6.32-{someversion}.el6.x86_64.rpm
reboot
The system will be running the 64-bit kernel which is compatible with 32-bit userspace.

rpm -q | grep 86$ | sed 's/\.....//' | xargs yumdownloader
rm *.i686.rpm
rpm -iv --force *.rpm
reboot

The system will be 64-bit.
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Note:
* If you have a working 64-bit system you can use yumdownloader to fetch the kernel and scp it to the 32-bit system instead of using wget.
* The rpm -q | grep 86$ | sed 's/\.....//' | xargs yumdownloader part could be improved to not download i686 RPMs along with the x86_64 ones.
* The *.rpm may expand to be longer than a command line can be. It may be possible to create a dummy RPM that lists all the required RPMs as dependencies in the spec file.

Why risk it - and have to deal with a Frankenstein flaky system afterwards.

Backup your data and config files, wipe the hard drive, do a fresh 64bit install, restore data and app configs, and be confident your new 64bit system will be stable.

I was hoping for something more specific than that but thanks anyway.

If I made two VMs, on 64-bit from the start and the other 32-bit converted to 64-bit and removed all the 32-bit kernels, and yum logs, syslogs, wtmp files, etc. and gave you root on both and asked you to tell me which was which I bet you couldn't (at least not without guessing and that would give you a 50% chance.)

I'm guessing a quick look at the default installed repo's will tell me which is which.

And that is your definition of a flaky system?

Moved to [i]CentOS Social[/i], as this thread does not contain a support query.

It's OK. Even if the question was in the support forum nobody here is smart enough to answer it.

I've been experimenting with this and run into one little glitch: at the point of installing all the downloaded x86_64.rpm files it rpm itself has a cow when the architecture of the rpm command changes. At that point I deleted the __db.* files from /var/lib/rpm , rebuilt the database with rpm --rebuilddb , and then reran the rpm -iv *.rpm command. So far so good, but I am still waiting for it to finish.

This old thread ended up being relevant to me out of a desire to upgrade a 32-bit install of CentOS 6 to CentOS 7 where there is no longer a 32-bit version.

Yes, I realize the a fresh install is the recommended way to go, but there is a special combination of curious and lazy involved in this experiment