Bismihi Ta'ala

It is permissible, but not appropraite nor suitable for a man to have a second woman in his Nikaah without the permission of the first wife. The problems that would arise are obvious.

Also, a person should be sincere if he wishes to marry a second time, and also very just and fair. He must also have the financial means for this and shouldnt do it for his selfish needs.

Although the Qur'an has permitted more than one wife, it has not encouraged it. Rather, it has set down a ground rule that if you fear injustice, then stick to one.

And Allah knows best.