Full-Time Employee Consultant for same Comapny

I’ve had an opportunity pop up where I’m currently employed.

I’m a full-time employee by day, 8-5, but I have a chance to work night-shift as well which is 5-midnight. As a full-time employee, I work for the corporate organization. At night, I’d be coming in as a consultant from a recruiting company that has been hired by the corporate organization, so technically, I’m employed by two different organizations.

Is this possible at all? I was unsure if there was any legalities behind being a consultant for the company you already work for.

Thanks for the help.