Zebra Finches have hatchling in nest... why are there new eggs in there too?

Hello! My new finches had bred, layed two eggs (but pushed one out of the nest). The remaining egg has hatched and our baby hatchling is getting very big! (It's now about two weeks old.) Today when I peeked in to check on baby bird, there are two new eggs in there. I don't want my pair to continue breeding -- I know it's stressful and I read somewhere to only let them lay two clutches a year. I also know that to prevent clutches, I need to remove the nest but how can I do that when there is still a hatchling in it? Thank you for your help! PS--> I have not checked to see that these eggs are viable... I haven't seen the pair breed recently. If they are just duds do I remove them? Not quite sure...