If, during an interview, you are told that the salary package provided is final. Is it possible to still negotiate?

I don't think it is advaisable to do so. You will have to decide whether to aceept the offer or reject it. If you accept the offer, I suggest that you clarify that you dont accept being on a lower package than you peers or staff in lower ranked positions. This will reserve your right to negotiate if you discover that this is the case.

At all times, remain polite and positive in your discussions about salary. Even if you're excited about the job but insulted by the initial offer, don't express your disgust to the employer and sound off about how much more you are worth.

Focus instead on communicating to the employer how interested you are in the job, and how much you know you can contribute to the company, and then mention that that are certain areas you would like to discuss before coming to final salary agreement.