Is it possible to configure logs per domain?

We have a WordPress multisite installation running on Litespeed. With many domains dropping activity into the logs, it's impossible to discern what site a particular line in the log is associated with. I've researched updating log file format, but I don't see anything that will include the hostname of the request. Is there any way to update log files from something like this:

[22/Nov/2022:22:31:56 +0000] "POST /wp-login.php HTTP/1.1" 200

to this?

[22/Nov/2022:22:31:56 +0000] "POST HTTP/1.1" 200

That didn't work for me - seems to just return the virtual host name but since we aren't setting up a new virtual host for every domain then that doesn't get me anywhere.

However I went down the rabbit hole of researching config further and I think I stumbled across a solution - %{Host}i

I haven't deployed it in multisite yet but is working to return domain of the request in a single site environment in my brief testing.