Jennifer if I understand you question correctly - the Accounting person is stored as one contact and the primary is stored as another.
If that is correct, then the best way I know to do this is through a “pre-populated” webform that you send them an email with a link to the webform for them to update. (use hidden field to identify, pre-populate and protect the email address of the original contact as the Contact ID is tied to that email address) https://help.infusionsoft.com/userguides/campaigns-and-broadcasts/campaign-goals/make-better-web-forms
The issue will be having that data update the primary contact record if there are changes. As these are 2 separate contacts within the application. The easiest and simplest way to accomplish this is to have a task assigned to someone if the webform is completed. There are ways to automate updating records through third party options, but not simple enough for me to explain here.
IF the contacts are stored within the same contact ID then it becomes much more difficult. Because Infusionsoft cannot “pre-populate” the form with details from the contact ID as they take that data from the email address and this would be a different email address from the main contact I assume. That will often result in over writing the data in the original contact.
So without more details on how this is setup in your app - I can’t give a complete solution.