"I have a fully remote position and want to take on a smaller contract position."
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Is it illegal to work multiple jobs at one time?
I have a fully remote position and want to take on a smaller contract position.

I’m not a lawyer, so I can’t tell you what’s legal or not. I can tell you that lots of people have side hustles. Lots of people also have non-competes and inventions agreements in their contracts that basically say that anything that you create while employed is the property of the employer.
I would read your employment agreement and talk to an attorney if it’s really important to you.
L2
I would also recommend checking company policy to see if there is something about conflict of interest and what steps to take.