You are absolutely going to get a different billing. You will have to pay a considerable amount of money to get the service set up in the first place. Since all three-phase installations are for businesses, they are all professionally installed and they will expect yours to be too.
If you are lucky the three-phase up pn the pole will be 480. (Many 240V machines can be jumpered to run on 480.) If not you will also have to pay some upfront costs for them to fit transformers.
If you're worried about the monthly cost of a second metering, I hope I am painting the picture that this is going to be costly.
Generally I hear this after someone has acquired themselves a fine deal on a machine tool on Craigslist. This is why it was a deal. As such, money is usually a serious factor, and spending even a mere $1000 provisioning service is out of the question for them. If that made you go "well maybe", you may want to look at a phase converter capable of converting 240V single-phase to 3-phase.
You don't want to mess with 208 3-phase. That is a compromise voltage used when a single service must provide all loads in a facility, and most of the loads are 120V, i.e. Residential or light commercial. It adds a neutral, giving a "wye" configuration, with 208V between any two legs. 208 is a compromise voltage and does not work nearly as well as 240V. it may be possible to boost it to 240.
If you must drive the entire building off one service, another, better, way to do at same thing is provision 240V "wild leg" delta. This is what you get when you add a phase converter to household power.