You have to disclose your work history on your SF85 for a Public Trust.
If neither company has a clause about not working multiple jobs AND (this is the big one) you’re not committing timesheet fraud (i.e. only so many hours in a day. You’re working one job 8-4, and the other job 4-12am), go for it.
This sounds like overemployment. You CANNOT take two full time jobs and work at the same time, especially with the federal government. They can and will charge you/fine you if they find out you are committing time fraud, and you will lose your security clearance. Do not even suggest you are planning to go ahead with this.
The non-gov would probably be ok with it if you get their approval ahead of time. As TheAwesomeJay123 so eloquently put it, the gov doesn’t allow you to double-dip your hours so they would probably say no unless you could convince them you won’t double-dip your work hours. You would have to segregate your hours (like maybe evenings and weekends) and document them carefully. Don’t see how you could do it, but maybe you don’t need sleep like the rest of us
You CAN, but are setting yourself up for some major headaches/legal issues including loss of both jobs, loss of your clearance, and if you commit time fraud, jail time.