There is a small branch, about 1/8 inch in diameter. Can I graft it above the caudex into an area that needs a branch?

Hi! If it is long enough to cut, then you can surely cut it and attempt to graft it to a different branch, but as far as I know, there is no way to graft a branch directly to a caudex. I may be wrong, but it also would open up a whole wide world of possibly damaging or allowing disease/fungus into the main structure of your plant, by cutting into the caudex for "no reason".

Maybe someone else will have a suggestion or further thought/knowledge on this, and can chime in.

I may be misunderstanding what you're asking all together.

Skipin,
Probably best to send through a photo, if you are able to.
I am getting from your post that you want to graft a piece of a branch to the side of the caudex to make the plant have branches evenly on it?

This possibly could be done, but it leaves so many different possibilities, with being able to visualize it, it makes it difficult.
It may just need pruning, bud grafting, etc.

Rick

Here is a picture. I want to move the small branch on the caudex up about 3 inches to the point indicated by the tip of the pen.

SkipinWV,
You could graft the small branch onto a branch above. If it is a grafted plant, then this branch would be from the Rootstock portion. Would be better grafting a small scion from a branch above then.
Rick