Dell battery upgrade

Hi everyone, I know this question might be a bit stupid, but I really want to know... Can you replace a laptop battery with one of a higher capacity? The thing is, I bought a second-hand Dell Precision 3550 for my studies. It had a 3-cell 51Wh 11.4V battery (which died), and according to what I've seen, there’s a 4-cell 68Wh 15.2V battery that Dell says is compatible with my laptop (based on their manuals and company specs). Is it possible to swap them, or is there a real risk of damaging my equipment?