I have a primary iCloud account that has a numbers spreadsheet in it and I would like to have a copy of that same numbers spreadsheet in a secondary iCloud account. It doesn't seem like this is possible unless I am missing something.
I log into https://www.icloud.com/#iwork on my Mac to log into a secondary iCloud account and upload / download documents since the Mac (as well as iOS devices) only allows one iCloud sign in per user account.
On iOS only, you can push the file to a general file bucket app and then sign out of iCloud, sign in to the new account, push the file back. This involves manual clean up, selection of another app, and manual signing in and out olympics so it's clearly not an ideal thing for anything but a very rare event.
On my iOS devices, both Dropbox and AirSharing are apps I use and would be ideal to hold an iWork document outside of iCloud storage while you are switching settings. I suppose you could attach the file to an email draft as well - but I prefer the above apps if you must do this only on iOS.