Asking You to Stay Beyond Your Notice. In this situation, you won't necessarily get the promise of more money or a better title__but your manager will ask you, perhaps as a personal favor, to stay a few additional weeks or months until the company is able to hire and train a replacement.
Prepare for It. Like the situation above, you should go into the conversation knowing how you'll respond if your boss asks you to extend your notice. If you've landed another job offer and have already set a start date, this may not be possible__so practice sticking to your guns: "Because I have a new opportunity lined up, my last day here is firm.