For an expanded set of genesis morphs, search ‘genesis evolution’ on the store, or click here. You can find an entire list of the expressions under the posing tab, with the head selected, and selecting ‘editor’ instead of presets. If you don’t see that tab in your interface setup, go to the top menu bar, and select window > tabs > posing.
The standard installation of the genesis figure does come with a fair amount of body, head, and expression morps. If the standard and the expanded sets of morphs don’t have exactly what you’re looking for, though, you can also create your own morphs in Hexagon, or Zbrush, if you happen to have it. Just don’t change the base topology, like adding or removing an edge loop, or you will turn it into a unique model, and loose the ability to use morphs and its original rigging information.
Most 3D software packages, like 3dsmax or Maya, have utilities for creating morph targets (or ‘blend shapes’ in Maya), but I’ve yet to experiment with exporting morph targets from either of those packages to Daz. Since using GoZ to take the genesis figure into Zbrush and back is so easy, I honestly haven’t had the motivation to try. However, creating morphs in Hexagon should be somewhat similar to Zbrush, since there’s a bridge between Hexagon in Daz, and the sculpting brushes will let you paint deformations in a similar fashion.