Q:

Add a new edge while keeping existing graph fixed

Consider the manually drawn red arrow in this graph:

I want to tell graphviz to draw an arrow like that, although the particular path is not important.  The important thing is that the existing graph not change at all.  Essentially, I want to instruct graphviz to

Draw a certain graph
Keeping that graph fixed, add a new edge to it

Is this possible?

A:

Yes, it should be possible.
If you have a certain graph (e.g. data.dot) and run this file through dot without specifying an output format, dot will output a dot file with added coordinates (attribute pos for nodes and edges). If you save this output (dot data.dot > data_pos.dot) you can add your new edge to it and you can generate your two output files.
You might have to enlarge the bounding box graph [bb="..."]; for the new edge not to mess with positions tho.

