Multiple male finches checking nest.
I have finches that have nested, and successfully had 2-3 chicks. (Wild birds) Now I occasionally see multiple males checking the nest. Once in a while, one chases the other away.
Are these wild birds outdoors? If so, it’s normal for other birds to investigate an abandoned nest. Some birds build a nest, others use an existing nest or cavity. Sometimes the male builds a nest and the mate has to approve it. Males can compete for females. And some birds are considered parasitic because they push eggs out of another birds nest to lay their own, and leave the other bird to raise the chicks. Regardless, I would leave them alone. It is actually illegal to interfere with a nest or even pick one up off the ground if it falls out of the tree.
If these are your own bird, then you should only have one pair of birds in cage for breeding. Other birds in the cage will be viewed as rivals. And rival birds will try to raid the nest of a breeding pair.
Thank you for asking Lafeber,