[North Coast Cab]

Start with the Utility. They will look at the feeder cable and advise on the Max panel you can draw off of it. If it needs to be upgraded it is not always easy....
Pulling the meter will kill the power into the house. You're typically responsible for everything from the meter in, although these days often the meter base is your responsibility. Be careful there as you may need a larger meter base as well.
So here' what I see could happen.
1) Utility feed can handle a larger service - you upgrade your main panel, run new wiring from meter to panel, and reconnect existing circuits.
2) Utility feed needs upgraded - following that you are in for the same new panel.
You coudl also hire an electrician who could place a recording meter on the main feed and measure the power draw over a 24 hour period.