If you have a nitrIte reading, although the tests are not accurate, its more likely showing lower than the actual nitrIte reading.
I wouldn't worry stressing the fish with larger or more frequent water changes because the nitrIte will kill them otherwise.
Not sure what fish you have, but if they have no problem with salt, you can temporary add 1tablespoon per 5 gallons. It will neutralize the toxicity of nitrItes(at least most of them) and help the fish breath, until the tank is stable. Make sure the salt is dissolved first and also keep up with the water changes. Once you dose the whole tank, only add the relevant ammount to treat the amount of changed water only. Salt doesn't evaporate.
This may help of the type of disease the fish have anyway if it is columnaris.