I work as an independent contractor, but thinking of taking a 2nd job as an employee. Is this legal? Would I submit self-employed (1099) + employee taxes (W-2) together?

At the moment since I only work as an independent contractor, I typically have to file a 1099 and a Schedule C. I'm guessing that if I decide to work somewhere as an employee, I'll just be adding a W-2 form when I file my usual taxes, but I'm not certain if that's all I would need or if it's even an option legally.