So I want to know what structures making an antibody species-specific? Anyway, I read about some experiments using the same antibody for capture and detecting, and just add an enzyme modification. So the answer is Yes?

If you are sure that the coated anti-human IgM (μ-chain specific) is specific enough to capture just the IgM, which it should technically, then I guess you can use the HRP-conjugated Goat anti-human antibody (H+L) for IgM detection with no hesitations.

But I would anyway run necessary controls to check for any potentials cross-reactions, which can give some background noise in your blanks, or you may end up with some kind of pseudo ODs.

Laharika Katamoni Many thanks to you! I think your advice really helpful. We have purchased the two antibodies, and I'll try adding some controls when doing another ELISA.