1. this offer may be not so good 2 .this offer MIGHT BE not so good 3. this offer may become not so good 4. this offer MIGHT become NOT so good The second and the fourth phrase were wrong, the modal verb is MIGHT (not "might to"), "May" and "might" have a very similar meaning, this is a link about the difference http://www.blogs.english4today.com/?p=26 I hope this could be helpful :)

We can use 'may' to ask for permission. However this is rather formal and not used very often in modern spoken English May I borrow your pen? May we think about it? May I go now? We use 'may' to suggest something is possible It may rain later today. I may not have time to do it today. Pete may come with us We use 'might' to suggest a small possibility of something. Often we read that 'might' suggests a smaller possibility that 'may', there is in fact little difference and 'might is more usual than 'may' in spoken English. She might be at home by now but it's not sure at all. It might rain this afternoon. I might not have time to go to the shops for you. I might not go. For the past, we use 'might have'. He might have tried to call while I was out. I might have dropped it in the street.