Hi Mike, there isn't any way for Fillet to do that, Fillet is pretty focused on handling all kinds of other situations like when 2 surfaces change angles to one another the length of the fillet arc cross section will become a longer or shorter length arc while maintaining the same fillet radius. It's just not set up to do something much different than that like you show there which would require some different method of generating the fillet rails. Also another area where filleting is complicated is when several fillets collide into one another and a corner patch needs to be generated.

Instead of fillet you could draw a circle off to the side, sweep a tube along the edges and use boolean difference, like shown here:
http://moi3d.com/forum/index.php?webtag=MOI&msg=817.8

Or if you are working on a flat shape something like a picture frame, instead of Extrude you can use Sweep on one rail path which will do mitered corners between each sweep segment, that looks like this:






If none of those match up with what you are trying to do could you maybe post an example or sketch of the type of result you're trying to build?

- Michael