When your not going a drastic color there really isn't alot to worry about in terms of the hair color, only thing is that it might not be as golden because ashy colors are really saturated. One thing to consider before dying your hair at all is the risk of damage or losing hair.
Make sure to remember that Ash hair dye has a green undertone, and if you put a golden brown over it, it may still have a green tint, so choose a hair dye that has a little bit of red to cancel out the green in the ash.
You want to make sure to stay within the same hair dye brands because you don't want to use a chemical component with a vegetable base. If you use golden brown on top of ash it might turn out dull looking, I would suggest using a high developer with it.