Ability to add modifiers to secondary claims only if not required by primary payer

Is there any way to get around the fact that the secondary payer follows primary payer set up?

For [a patient], we need discipline modifiers on the secondary claim. Other than manual intervention, the only way to do this currently is to turn on mods for the primary payer. However, primary will deny if the mods are on the claim.

We've always been told that secondary follows primary set up. Is there any way to get around this? Not all settings apply to both payers and do cause us issues on the backend.