You can't. The format for
/etc/hosts is quite simple, and doesn't support including extra files.
There are a couple approaches you could use instead:
Set up a (possibly local-only) DNS server. Some of these give a lot of flexibility, and you can definitely spread your host files over multiple files, or even machines. If you're trying to include the same list of hosts on a bunch of machines, then DNS is probably the right answer.
Set up some other name service (NIS, LDAP, etc.). Check the glibc NSS docs for what is supported. Personally, I think you should use DNS in most all cases.
Make yourself an
/etc/hosts.d directory or similar, and write some scripts to concatenate them all together (most trivial:
cat /etc/hosts.d/*.conf > /etc/hosts, though you'll probably want a little better to e.g., sort), and run that script at boot, or from cron, or manually whenever you update the files.
Personally, at both home and work, to have machine names resolvable from every device, I run BIND 9. That does involve a few hours to learn, though.