If you use an internal proxy server1 and have many computers represented by a single IP address, a bit of caution is warranted using the block feature. Since block works for 24 hours on the given IP, you do not want to inadvertently block more devices than the single problematic one.
Proxy servers can be configured to send x-forwarded-for headers. When this is done, the chat will be represented by two IP addresses instead of just one: one IP for the proxy and one to represent the specific device. In this way, blocking will only impact the single device instead of everything behind the proxy.
1 Here, "internal proxy server" means the kind used to boost performance on large networks, not a proxy server such as EZ Proxy that is used to facilitate remote access.