Use the Recipient Type of either Specify Recipients or Update Recipients based on the Use case. I could not give you specifics on how that is accomplished through an API but this is what I would do if there were unknown Recipients and they needed to be defined by another individual.

Thank you for your answer. Would this allow the initial recipient to choose themselves as the two later recipients? If they chose themselves as the recipient for the later two sections of the document, would it still send them various separate docusign emails to fill out each section of the document, or could they fill out the entire document from the initial email if they choose themselves?

Lets say you have 4 potential Recipients who would need to sign. You know the first so they are Recipient 1/Signer 1, you know the person who knows who Signer 2, 3 and 4 will be, no matter who, even if they were already Recipient 1. So Recipient 2 is set to Recipient Type of Specify Recipients. They are notified after Signer 1 completes, then they add or specify the remaining Recipients. The notifications would work in the exact same way as if you set the Recipients in the envelope. Once each Recipient completes an action the next Recipient is notified (as long as you use Signing Order).

So the first person in your scenario, if they were the person filling out all sections of the document, would have to receive 4 emails prompting them to sign, to fill out the one document? It almost starts to feel more convenient to just not use Docusign for this document.

Use Collaboration feature or Data Labels to replicate data, or Markup to allow document editing. Also I would investigate and streamline a process, I have found processes sometimes to include steps that make no sense whatsoever, they have just been around so long that they feel they cannot change. Also as a Sender you could create a Template and when you use that Template, the Sender could fill out everything but the Signature blocks and uncheck Read-only allowing the Recipient to make edits during their action. Also any Sender or Recipient can change Notifications and manage their workload by DocuSign Inbox.

There are times when additional steps might need to be taken for a document to get signed electronically but as mentioned I start looking at the process to understand the "why" instead of the "how", which might make the "how" better.

It's not really a process problem I don't think. There is no alternative way I could structure the document to make it require fewer signers. Allowing the signer to edit the document would also not help in any way I can imagine. Its a customer application that requires a) company information. b) someone who can sign as the ongoing sales contract signing authority. c) someone to cosign for their company if necessary to be extended credit. These may or may not be the same person, depending on the customer.

I like the idea of an initial recipient that can determine who fills out each section, but it sure would be a lot smoother if that when the initial recipient assigns all three sections to themselves, for them to just be able to fill out all three sections then and there without going through three additional emails/signing processes. Not sure why it would not behave that way.

Another option I thought of was Templates, and having multiple Templates that could act as overlays to save time. But remember you can have Recipient 1 fill out multiple sections even if that section is being signed by someone totally different, it really becomes a validation that the data entered is correct in that section, hence using collaboration. So in my example Recipient 1 fill out section 1 and section 2 and section but only signs section 1, then Recipient 2 does specify, and then it rolls to Recipient 3 who signs section 2 (but doesnt have to' fill out text fields.)

Are there additional settings that must be switched on to use 'Specify Recipients' or  'Update Recipients'? When i add a person to the document, my only options are 'Needs to Sign', 'receives a copy', and 'signs in person'. Thanks

As a DocuSign Admin these options are under "Sending Settings" then Recipient Roles section there are items to enable...

Enable needs to view role

Enable specify recipients

Enable allow to edit recipient

Enable update recipients

Enable in person (hosted) signing role

However, if you do not see these options, then as I understand it, these Manager Recipient types they are enabled by the Account type and feature set of your DocuSign Account, so you would need to talk to your Account Manager or a Sales rep in case its required to upgrade to a different DocuSign account type.