I had multiple electricians come out. All of them said I would have to upgrade my service to at least 300 amps in order to install a higher amp circuit in my garage. I have 3 completely independent HVAC systems, two full size ovens, one electric range, two full size refrigerators, two microwaves, a dryer and outlets, lighting, etc. for about 5,500 square feet of finished living space. The electrician calculated the total load (excluding any EV charger), and I was already at 240 amps. With my existing 40 amp EVSE line that put me at 280 amps.
I am in the process of having the service upgraded to 400 amps total. I will have a 100 amp circuit in the garage connected to the Tesla Wall Connector, and I'm keeping the 40 amp line that was there previously as a backup for a second EV later down the road since the circuit was already in place. I just had the service center order the parts to upgrade my car to the 72 amp charger. All in it will be about $11,000 for the service upgrade and upgraded charger, but it will let me charge almost three times as fast as I can now.