No, you cannot sync the logs to multiple accounts. The account that is being used, you can view / sync logs of that particular account. Every time you switch accounts, you can sync logs of that particular account.
For instance, if you have two MyOperator accounts namely, A and B. You can view the logs of the each account separately. Logs of account A won’t be visible in B and vice-versa.
This helps you eradicate confusion and mixing up of contacts. If the nature of the businesses are different, it is better to keep their data in separate accounts.