Hello @Melanie_Dailey ,
If the organization's list is a wholly separate account from yours, then no. Unsubscriptions are only on an account basis.
If the other "organization's CC list" is within your account, then yes an unsubscription would apply to the entire account.
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Using the Update Profile system, you can include this as an alternative link in your email footer, which contacts can select to update their list membership, based on the lists you make viewable and editable. If multiple list options are available in your UP form, those options will also appear on the unsubscription confirmation page, as an alternative for contacts that click the unsub link in the footer.
Remember that not all lists need to be included in the UP / unsub setup. Contacts will only be able to manipulate their list membership for the ones you've explicitly selected to be available, viewable options. Contacts will simply see those available lists' names on the UP form / unsub confirmation page, and be able to decide if they'd prefer one of those.
See also:
Unsubscribed contacts overview
... View more
