Can I work as 1099 contractor while working w2 job

Hi 

I am currently working remotely for an employer as a full time employee on W2 with benefits.

Although it's a full time position I have bandwidth for taking up another remote job.

 

Can I take up another full time job as 1099 contractor or is it illegal?

 

If there is no problem, then as an independent contractor should I start an LLC? Please suggest. Thanks!