Should I support IE compatibility mode?

Question

So I have a client that is running multiple versions of multiple browsers. I currently support IE7, IE8, IE9, Firefox4/5, Safari 5 and Chrome. The site works in all the named browsers.

IE has a feature called 'compatibility mode', the current bane of my existence. The problem is that in compatibility mode, form buttons work differently. I won't get into the details but it would be a major effort to make the site support 'compatibility mode'.

Is this something that there are frequent requests for? Am I off my rocker to push back on the client and tell them this just isn't an option?