Is it permissible to marry for a second time in another Islamic country while the first wife remains, in the event that polygyny is prohibited in the home country, and what are the necessary procedures for that?

It is permissible to marry in another country, but the procedures differ from one country to another. It is also permissible to marry without documentation in court if the marriage fulfills its Sharia conditions and pillars, in order to prevent harm and without the need to travel.