Uh, what do you mean? Different IP of the players with the same nick on your server? If the server is yours then so are the rules, personally I think it's nothing serious.
You define rules at your own server; you decide, what is good and what is evil.
Basically, you should ban people who spoil fun for others; but once again, it's your choice, what is 'spoil' and what is 'fun'.
Different people have different opinions about that.
There is nothing wrong when somebody comes with new ip address; a lot of ISPs (including the one I use) have a 'dynamic IP' system, where user gets a different address each time he/she reconnects.
Though dynamic IPs of same ISP always belongs to the same range.
Also, it's a normal situation when two or more individuals have same IP, since a lot of ISPs implement a NAT system -- there are not enough ipv4 addresses already.
You shouldn't ban people those simply use different IPs, if they behave normally and you have no reason to think they are bypassing a ban.
You should ban players who change their IPs to bypass an existing ban.
Generally, there is no way to detect an actual person on your server; IP can be changed by reconnecting or by VPN, nick can be easily changed from in-game menu.
Servers owners are forced to rely on analysis of play style and chat activity in order to reveal perpetrators those are banned, but found their ways to play.
You are on your own.
If you ban some IP, you ban not only guy you want to ban, but also everybody who share an IP with him.
Although it is not necessarily that there is a second MBII player from same address.
If you ban some IP range, you ban all people those use that range. Collateral damage is possible.
Once again, it's possible that there are no other MBII players those have that IP range. You never can tell.