I'm going to fill out Rate Limit Adjustment Request - Formstack but since there's a couple week response time I was hoping in the meantime to get a rough answer of what I could expect. What maximum request volume has typically been accepted? Would ~40k be considered?
Most of the largest Certificates per Registered Domain rate limit adjustments have been given to organizations like universities, where there are administratively or technically independent entities inside the organization that are requesting certificates under its domain (like someprofessor.math.example.edu, someresearchgroup.humanities.example.edu, somesport.example.edu...). These entities are probably not all using the same server infrastructure or IT.
If you're requesting 40,000 weekly Certificates per Registered Domain, you should probably have thousands of people or groups who, using their own servers, independently request certificates from Let's Encrypt.
Another case which has been discussed here is a product where each instance of the product, after being purchased by an end user, requests its own distinct certificate under the manufacturer's domain name. These devices should not share private keys because they're not operated by the same person or organization. This might be something like a NAS server, a home automation server, a webcam, or maybe a network router.
Still another case is a cloud hosting provider which operates a large number of servers on behalf of different customers and wants to give each server its own name with HTTPS access. If these servers are operated directly by the hosting provider and not by the customers, the provider might be asked to consider issuing certificates that cover more than one name and sharing certificates across multiple servers.
You'll have to explain what you plan to do and why you need such a high volume of certificates, and why the certificates should not be shared across servers or devices. "They are in fact run by entirely different people" is a relatively good kind of answer there; "there are just so many of them" is a less good kind of answer.