Dear Kylie Smith:
The specificity of haemagglutination inhibition assay (HIA) for the
detection of influenza antibodies in sera can be considered to be
very good because the HI antibodies are induced by the viral
haemagglutinin (in the surface of viral envelope) which determines
the subtypes of influenza viruses.
Although many viruses, especially the myxoviruses, have haemagglutinin
in their envelopes, you will not confuse when you are doing HIA
because the standard virus strains must be used as the known antigens.
No further control is needed except the haemagglutination control.
Happy New year!