It would hurt like hell.
Concussions are cumulative. That is to say, the brain gets bounced around and is injured in the process. Those get considerably more dangerous as they pile on. So a second concussion is going to be much more dangerous.
To be fair, all injuries are cumulative. It’s not something we frequently focus on, because the actual immediate danger doesn’t ramp up as much, but it is still there. Getting tagged in a bruise will hurt more than taking a blow to uninjured tissue. Generally it’s not significantly more life threatening, but continue abusing injured tissue, and things will get worse.
Strictly speaking if you suffer blow to the head and end up with a bruise there, then take another blow and end up with a concussion, the injuries are actually unrelated. They don’t stack together. They are different injuries. One is a ruptured bloodvessel in your scalp, leaking internally. The other is damage to your brain.
The unusual issue with concussions is the human brain; it’s not great at healing. It will heal over time, but in comparison to the rest of your body, it takes much longer. So concussions stack together the way they do, because the injuries linger.
So, yes, injuries do stack together. But, as we’ve said before; blows to the head do not equal concussions. Taking a blow to the head that doesn’t result in a concussion doesn’t increase the risk of receiving a concussion, the way suffering a concussion does.