I've been asked to make some fairly significant changes to our web site, but the site will overall have the same feel. I'm wondering if I should modify the current customized Genesis child theme, or if I should create a new child them. Any thoughts?
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I do agree with Aaron's thoughts on "It all depends on the amount of changes required".
Still. I would use a slightly different work-flow. Meaning:
This way you get both worlds: You get to have a brand new child theme and get to keep all the useful modifications you have already so hard worked for. And the best deal? You can try it out without loosing a single visitor when combined with a plugin like Theme Test Drive or even try them out from your Appearance->Themes screen.
You can even have 2 or 3 or 5 child themes with minor modifications.
Hope that helps, marikamitsos
It all depends on the amount of changes required, as well as whether or not you plan on keeping the theme you'll be editing 'up-to-date' with the theme author's releases. If, however, its a custom built theme, then I'd stick with the child theme you're in.
Generally it'll be quicker and easier to modify the theme you're in then create a child theme of a child theme and try to have changes passed back or run the risk of completely overwriting files like header.php.