I have read that, whilst not always supported by all browsers, it is possible to have a wildcard certificate for sub-subdomains - i.e. signing for *.*.example.com.
Is this something that is supported at all in Let's Encrypt, aside from any technicalities with certbot or similar in performing the renewal process? Do Let's encrypt sign wildcards for more than one level of subdomain?
I came across this with a client at work, and however they managed it, they did get it sorted with their CA in the end, so from memory I think I have seen one in the wild.
I see a few mentions of it through google; IIRC, some workarounds are possible but not always successful.
Only *.example.com style wildcards are permitted by the baseline requirements, where a * is immediately followed by a . and then an otherwise fully-qualified domain name.
Thus the following aren't permitted:
*foo.example.com - needs to be a . following the wildcard foo.*.example.com - * must be the leftmost label
Other combinations like *.*. are also not permitted.
Wildcards also can't be used for a "Public Suffix" like *.com or *.co.uk
formats not permitted: some*name.example.com somename*.example.com *somename.example.com
other reasons a wildcard cert won't be allowed/issued: has too many dots [in the case of LE = only 10 dots in the FQDN part of the name are allowed] has too long a name [in the case of LE = only 63 character (including dots) length are allowed]
permitted: *.[plus a "normal/valid" FQDN] *.somename.example.com *.some.really-long.folder.name.with-dash-es.example.com
Wildcard Domain Name : A string starting with "*." (U+002A ASTERISK, U+002E FULL STOP) immediately followed by a Fully-Qualified Domain Name
Fully-Qualified Domain Name: A Domain Name that includes the Domain Labels of all superior nodes in the Internet Domain Name System.
Domain Name: An ordered list of one or more Domain Labels assigned to a node in the Domain Name System.
Domain Label: From RFC 8499 (RFC 8499 - DNS Terminology): "An ordered list of zero or more octets that makes up a portion of a domain name. Using graph theory, a label identifies one node in a portion of the graph of all possible domain names."
It's a bit of a mouthful, but as the others said, it boils down to: if there is an asterisk, it can only be at the very beginning, immediately followed by a period, and then a "normal" (i.e. no more asterisks) domain name.