About christians and muslims marriage, legality and morality.?

i am shock about the christians who are married and using muslims traditions to be able to marry more. for ex. a guy who is a christian is married to a woman who is also a christian. but as time goes by, this man want another woman who is also a christian. of course it is not legal for them to pursue their relationship bec. the man is legal married (his wife) but this man is this 2nd woman use muslim tradition, they convert themselves into muslims ( in muslim you can marry a womam more than as you want as long you are capable of marrying it and of course with the consent of the original wife) so this man and 2nd woman became islam and they married in muslim. the questions is what will happen if the original wife who is christian will protest about the situation. who has the right? this is from philippines. want to know about your thoughts here, especially legality. thank you