No, the database schema prevents this. You would have to find a different way of doing it, like adding your own property and filtering your menus on that instead.

As Magnus says do your own property and do the filtering yourself.

Create your own filter and then make your own versions of the EPiServer webcontrols where you override the post filter method and add your own filter as the last one. This way you can use the Epi webcontrols but they automatically run your filter.

Ofcourse if you use repeaters or such you need to use the filter directly.

Well, ok. Only problem then is that the user have to keep track of another property and i think it could be confusion to have a "custom" property that does basically the same thing as Show page in menus.

Oh well, back to the drawingboard. =)

You could hide the old Show page in menu, and only show your own.

You need to attach to the DataFormProperty.Populate and hide the orginal one.
Take a look at http://www.slideshare.net/EPiServerMeetupOslo/episerver-behind-the-scene page 12 for how to