Morphing

Although Unity can import meshes and connect the rig together, morphing is not supported. Options like a weight-slider  to toggle between the mesh of an overweight person and a mesh of an underweight person are difficult to achieve in Unity.

One plug-in available in the Asset store could achieve this goal but note that the asset isn't free.
Mega-fiers can be found here.

A Basic Character Creation System

Unity supports numerous options for a character creation system. A basic setup could be the option to change class or gender. When the class/gender is chosen the mesh is instantiated on to the stage and from there on details can be changed or added. Things like shoulder pads and  ornament are easy to set up.

More complicated geometry such as an armor that wraps around the torso requires the armor mesh to be exported along with the rig for the character.

When the character is edited and ready for the game, the script needs to clean up the model. If you had imported an armor with rig the rig needs to be baked. This prevents the game from loading two rigs that play simultaneously and with that data going to waste.