I'm new to systemd, so I tried overriding a unit file by copying it to /etc/systemd/system/multi-user.target.wants/ directory and editing it there.
That was a mistake, the proper path to copy unit files is /etc/systemd/system/.
However it took me a decent amount of time to find out, since everything I tried was failing with the following message. Google gave me the answer, but as an admin I like to search things on my own. Strace'ing systemctl didn't help (it sends messages via socket) and I still don't know what was the dreaded method call that failed...
# systemctl reenable MYSERVICE # Or almost every command on MYSERVICE
Failed to issue method call: Invalid argument
The failing reenable is actually discussed here.
*** This bug has been marked as a duplicate of bug 880353 ***