Is there a way in Marketing Cloud to set up a rule, whereby all outbound messages are copied to an internal compliance email account? I know the Salesforce has this feature, but I could find no such feature in Marketing Cloud?
There is Email Archiving available: https://help.salesforce.com/articleView?id=mc_es_email_archiving.htm&type=5&sfdcIFrameOrigin=null
Or you could do what we did once, set up a separate inbox and BCC this inbox on all emails you send - but you need to remember to include the BCC email address on every send in your account. This would cost you an additional message for each email you send out.