An LLC can certainly operate under more than one DBA. But you’re right, it could become an accounting nightmare, even if you are absolutely meticulous about how you categorize income and expenses. That's because all the money would be flowing in and out of the same company, even if with different bank accounts.

If one line of business (DBA number one) happened to be doing poorly, it would adversely affect the fortunes of DBA number two --because, again, it’s all part of the same company.

It would be best to speak to your accountant--or whomever would be handling your books--to see if your scheme could be handled easily or if it will cause unnecessary headaches (and markedly increased bookkeeping and accounting fees).