It is possible , Mini Mania UK has a customer who has obtained 228 bhp from the Cooper.
He used 4 throttle bodies,and reverted to a cable from the pedal, also used an aftermarket ECU from DTA in Manchester, ( Motec could also do this) , used the Minimania cylinder head with our big valves , he did however use titanium rods /crank (custom,) and a lot of other internals -pistons, rings, and he runs at 11000 rpm.
When finished he spent a lot of money to get 228hp
The bigger valve head and billet race cam (skimmed a bit for higher comp ratio) would push him close to 170 (stock rpm) -and would make more than this with raised rpm limit in remap 7200 rpm -this would require also
1 oil cooler
2 aluminium rad -too allow the 7200 excess heat
3 4-2-1 header
4 larger throttle body
increased springs in head and retainers-all available
I would also suggest light weight fly/clutch and use the S 6 speed
over 180 would result -(5 speed suffers around this mark)
intake manifold breathing restricts output to 180 ish -unless throttle bodies fitted
All reported from Adam at Mini Mania UK