What if we file an Offer and the IRS calculates a higher RCP amount?

The IRS will generally allow the taxpayer to respond and show why the IRS is incorrect. If the IRS is correct, the taxpayer should be allowed the opportunity to agree and amend their Offer to increase it to the IRS calculated RCP. If the higher RCP means that the taxpayer can full pay within the time remaining on the collection statute, the IRS will recommend rejection of the offer.
If the taxpayer had filed a lump-sum Offer, the taxpayer will be required to submit the additional 20% due, given the increased Offer. If the taxpayer filed a deferred Offer, then the increased amount will need to be made up in the future monthly payments.
Also note, that in agreeing to sign an addendum to their Offer (IRS Form 14640), increasing the amount of the Offer. In addition to the addendum the taxpayer will be required to submit an additional payment to reflect the increase in the 20% initial payment that should have been made. Once this is done it will be submitted to management with a recommendation of acceptance, but there is no guarantee management or IRS counsel will agree and sign off on an acceptance of the Offer. Clients need to know that the addendum does not guarantee success.