You can migrate most of it. You can't move the email account or photo stream photos, and you have to recreate any synced notes in the new account.
To migrate a device to another account, start by saving any photo stream photos that you want to keep on the device to the camera roll (by opening the my photo stream album, tapping Edit, tap the photos, tap Share, tap Save to Camera Roll). Then go to Settings>iCloud, tap Delete Account and choose Keep on My iDevice when prompted. (This will only delete the account from this device. Other devices keeping the account will not be effected by this.) Then go to Setting>iCloud and sign in with a separate Apple ID to create the new account. (Note: you can continue to share the same ID for iTunes if you want; it does not need to be the same as the ID used for iCloud.) Turn on your iCloud syncing options and choose Merge to upload the data to the new account. When you turn on Mail, you will be asked to choose your new @icloud.com email address.
If you want to recreate any synced notes in the new account, open them one at a time on your iPhone and email them to the new @icloud address. These emails can be opened on the other device and used to recreate notes in the new account.
If you are migrating other devices to this new account, you will only need to save the photo stream photos to the camera roll, then delete the existing iCloud account, choose Delete from My iDevice when prompted (since the data is already in the new account), then sign into the new account ID and turn on your iCloud syncing to sync the data to this device.
When you're done, you can go to icloud.com from your computer, log into each account separately and delete any data that you no longer want from each account.