A broody hen is a feathered paradox, equal parts devoted mother and feathered grudge-holder. When one of our readers, /u/SpinachReasonable262, finds themselves in this very situation, we feel their confusion. Three eggs marked with an "X," more eggs appearing, and a hen who refuses to budge. It's a cluck-tastic puzzle, but we have some egg-citing clarity to offer.
First, let's address the egg-stra eggs. Yes, remove them. Your broody hen is committed to the original three, but her roommate, or even she herself, may keep laying new ones. Those newcomers won't hatch on the same schedule, and they'll only confuse matters. Marking the originals was a smart move. Now, gently lift her (she will grumble, consider it her love language) and take any unmarked eggs. She won't abandon her nest for this; she'll settle back down once you're done. As for whether she'll stop laying once she's fully broody, the answer is yes. Her body shifts gears from egg-production to incubation mode. No more eggs from her until the chicks arrive or she gives up the ghost.
The real worry, will she abandon the first chicks to hatch while the other eggs die? It's a fair fear. Hens are not perfect multitaskers. Once a chick hatches, she'll focus on that peeping ball of fluff. The remaining eggs may get neglected, especially if she leads the firstborn away from the nest. The practical fix is to move her and the original three eggs to a separate, quiet space before any hatch. That way, she stays put until every egg that's going to hatch has done so. No fowl play, just a little planning.
You don't need to be an expert to handle this. You need to be a little bold, a little patient, and willing to ruffle some feathers. Mark your eggs, remove the extras, and give her a private nursery. Your broody hen will do the rest, grumbling all the way. And when those chicks arrive, you'll have earned the right to say, "I told you so."