It is possible, but it does require a little bit of setup.
- Create a profile attribute named CCAddress (It can be anything, just using CCAddress for this example). It is probably a good idea to mark this as Hidden so it doesn't show up on the default profile center if that is being used.
- Modify your Triggered Email definition (Email > Interactions > Triggered Email) so that the CC field reads:
%%CCAddress%%. You may need to pause the definition before making changes if it is running.
- Publish changes and restart the triggered email.
- In the REST call, pass the address that you want to receive the CC in under the SubscriberAttributes section with a key of CCAddress, example:
I just tested and I can confirm that this works. Same concept would work with BCC as well.