Q: Is it possible to add additional providers to cc in the cc box beyond the options (e.g. current provider, referring provider 1, 2, 3, patient etc...) that are currently available?

Yes, in versions prior to V11.4, this can be done in the Patient Profile Dialogue form under Associated Providers. When set up, the providers are defaulted as cc providers per patient.
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Version V11.4.1

Anyone added to the Patient Care Team section of the note will be available to carbon copy.