As sources say, the Cosmic Microwave Background originated as the first electrons and protons recombined in the early Universe to hydrogen atoms. The resulting $\approx$ 13.6eV photons enlarged hugely due to the expansion of the Universe are now the CMB.
However, that was not the only recombination process. For example, about 25% of the young Universe was helium, thus there should have been two additional reactions:
$$\alpha + e⁻ \rightarrow \mathrm{He}^+$$
$$\mathrm{He}^+ + e⁻ \rightarrow \mathrm{He}$$
Beside that, some deuterium, tritium and $\mathrm{He}^3$ also was created, with a slightly different recombination spectra.
Beside that, also higher order reactions should have happened, like the creation of $\mathrm{HHe}^+$ ions, $\mathrm{H_2}$ molecules, and so on.
These reactions happened with a different reaction rate as the Universe cooled.
I think, the result of all these should have been a complex spectrum.
However, the CMB has a nearly perfect black body spectrum.
Why?
Where are, for example, the radio photons coming from the initial helium recombination?