I bet you could do it.
Make a new neck, saw off the old neck and attach the new one with a double spline joint. Take the bridge off and replace it with a longer one, it becomes a kind of brace cross grain being wider.
Perhaps take the back off and shore up the upper bout under the top or not...depending.
You could also do something goofy like cut out some wood lengthwise down the neck on both treble and bass sides and splice on material to widen the neck and reshape the neck. It might look funky, so paint it a dark color. Then fill and add wood to the head stock to get the Swan head thingy like a theorbo.