I actually have 3 phase in my home. Notes you said it was not possible. Not sure why, but it is here. Why would anyone ever want it?
Three phase power distribution is used in cases, such as industrial setups, where large motors or other loads are attached to the AC power mains. The advantage of 3-phase over single or two phase is that more net power can be delivered to the load over a 3-phase system for a given conductor size.
If you happen to actually have 3-phase power delivered to your site then it is possible that a previous owner or site occupant had loads of the type that demanded the more efficient power transmission.
Three phase power installations use a different type of main load center distribution panel than a single or dual phase system. Thus it is not a good idea to even think of mixing the two.
Here's an example:
My home was provided with a three-phase supply when it was built in 1990 because the builder intended to install an electrical storage-heating system.
I bought the house before the heating system was installed and opted for an oil-fired system instead.
So, in my area, it's an option you can request from the power company if you have a specific need for it.
So far as I know, three-phase supply is commonly used for equipment that requires substantially more power than most domestic household appliances. Some industrial electric motors require a three phase supply. In my area a single phase is 230 V so domestic households almost always use only a single phase. I expect the phases are separated at the local substation where high voltage local distribution is reduced to 230 V.