Is it legal to work in 2 private companies together? One is part time.

As you are working with a Private Firm, your employment with them and elsewhere will be governed and controlled on the basis of rules and conditions laid down in the terms of your appointment with your employer, which you must have agreed upon by duly signing & acknowledging an Appointment letter while accepting the employment offered by them.

While majority of the Private Employers have a standard condition wherein they do not allow any other employment (part time / freelance / contractual / etc.) while you are employed with them, you have to go through the provisions of your Appointment letter and in case those provisions do not prohibit you to be employed somewhere else during your off-time, then you may take the written consent of your full time employer to proceed and accept any other employment offer. 

Similarly, you have to inform the employer where you would like to be engaged part-time and also take a written permission about your engagement with some other employer for full time, to obviate any legal tussle in future with any one of the employers.