Can I branch off my main service, just past the meter base?
Yes.
You can buy a meter disconnect all in one like this one.
I personally would not buy the Leviton  but this is just an example.
You just need to pull a permit and order a disconnect from the city.
Just check with your local authorities that you won't need to upgrade to a 320 amp service.
As far as 2020 code goes you'll need a sticker that says emergency disconnect since this meter has a main breaker.