Such folks normally designate one property as their "primary residence", commonly defined as a place where one sleeps 183 nights out of the year. That's where one pays local taxes.
So it's somewhat possible. Interesting what to do if one have three properties and you 'sleep' in them 1/3 of the year. More complex question about 'digital nomads'. I personally live in one place for many years already. But I'm curious what people do in more dynamic housing situations.
It's definitely not possible to have a mail forwarding box as your primary residence.
> But I'm curious what people do in more dynamic housing situations.
In situations where a primary address is ambiguous based on number of nights, many tax authorities will consider other aspects, such as the address you have listed on government documents, where your family lives, whether you use any of the properties for income or pleasure, where you work, etc.
Also, if you change primary residences, many tax authorities will simply pro-rate your taxes for the period of time that you lived there.