The male seems not at all troubled. An extra female will do just fine. But his first female flies into a rage, threatening and driving off the intruder. She wants the male all to herself.
There is clearly a conflict here, between the male and his first partner. They have different ideas about the second female. But the male has another way to acquire a second mate. This is what he does:
When the first female lays her eggs, she is tied to the nesting box. Then, her mate disappears. He finds another nesting box out of sight of the first, and then starts singing to attract a new female. She mates with him and lays her eggs.
Now he disappears again, back to the first partner as though nothing had happened. He spends most of his time with her, helping to feed their young.