There isn’t a particular limit on number of domains per week. If you have a truly enormous number of domains – like, millions – you may have trouble with the Pending Authorizations and Overall Requests per second limits, but it’s difficult for most users to issue that many certificates that quickly.
There’s a limit of 20 certificates per domain per week.
That’s discussed at the link at the top of this post:
If you are a large hosting provider or organization working on a Let’s Encrypt integration, we have a rate limiting form that can be used to request a higher rate limit. It takes a few weeks to process requests, so this form is not suitable if you just need to reset a rate limit faster than it resets on its own.
Note that most hosting providers don’t need rate limit increases, because there’s no limit on the number of distinct registered domains for which you can issue. So long as most of your customers don’t have more than 2,000 subdomains on a registered domain, you most likely do not need an increase. See our Integration Guide for more advice.
May i ask which limit(s) you’re running into, and why?