Child of a child theme
Yes you can do this.

I often use zen as a base theme and have some common things that are always in the sites we're building, so we have a common sub-theme theme of zen, and then each site has a sub-theme of the common sub-theme.
For things like this it is great to use this kind of setup.

So you have:
Zen > Zen sub-theme > Zen sub-sub-theme

In the sub-sub-theme the base theme would be the sub-theme. 

For more detailed information on how it all works, see the Creating a sub-theme page.