One way of building a higher output 850 would be to use a 970 'S' block, crank & rods, then reduce the bore by sleeving and fit suitable pistons, assuming some can be found at the right diameter (I've not looked for any).
That would be an 850 Cooper 'S' engine with a 12G940 head. Not something suitable for road use and in competition the regulations might not allow this.
Disappointment might result from 850 tuning a whatever you do it's still going to be slow as it's hard to get any meaningful torque figure and that is what bestows overall performance, not maximum bhp.
I'm currently restoring a 1964 850 and it will be more or less standard as I can't see the point in putting extra cash into what will simply be a slow and old classic car (but great retro driving!).