"I'm not a chassis engineer but I think you will reach a point where too much rigidity will have a negative effect, so don't go overboard with the stiffening."
"The Setup is much different to the 4stroke."
Too stiff is easily achievable.
There is definitely room for improvement (especially with supermoto) in the rigidity of those frames, but make it too stiff/rigid and the bike will start to loose feel at high cornering speeds (higher g-forces).
The lower cradle is a great place to start. I would also be looking at other motor mounting areas, suspension mounting areas, and any area/section of the frame where the flex that is required may be influenced by outside forces/mass (like the motor, suspension, pegs, etc.)
1993 Honda VFR750F
2006 Suzuki DR-Z400SM
1988 Yamaha RZ350 (sold)
"Not now officer, I'm on the clock!"