ANSWER:
This is permissible, however it’s not recommended as the man would have to lie to his first wife about his whereabouts when he’s at his second wife’s house and it’s a major sin to lie. And the problems would escalate when he has children with his second wife and more so if he dies and the issue of inheritance would come up. Besides, everyday he keeps this as a secret from his 1st wife, the more betrayal she feels once she gets to know and she would hardly forgive him for that.