Preset widget configuration?

Within Multisite, is there a way to have a pre-set widget configuration assigned to each theme? For example, if a new subsite activates Theme 1, it would automatically load the proper widget configuration for that particular theme. Then if the user switches to Theme 2, it would automatically load a different widget configuration? Does WPMU have a plugin or way to aid in this approach? I thought I'd ask here, since everything here is geared toward multisite. I'm not finding a good way to address this.

The goal is to make switching a theme not require an all new set up every time. I'd like users to be able to select a theme and be up and running. They'd be able to customize further of course, if they wish, but switching to a new theme wouldn't totally wreck their layout.
Any insight is much appreciated:slight_smile: