Dr. Rajab Abu Maleeh, Ph. D. in Sharia, said:
Yes, it is permissible for a Muslim man to have a second wife abroad if he is in need of that. Keeping the second marriage secret from the first wife is also permissible if the he fears of consequential problems, but this may cause him to be unjust with regard to giving both wives equal rights.
Taking a Second Wife in the West