Every Griffon engine from the Mk 61 on had a 2 speed, 2 stage supercharger, except for the Mk 101, 102, 105, 121, and 122 which had a 2 speed, 3 stage supercharger.
. It would appear then that the Spitfire XII
was never given a larger diameter impellor or settings to raise its
high altitude performance. Possibly because the two stage
Spitfire was available. It quite a good idea, the Soviets would
have love clipped,croped and clapped Spitifres.
The XII was only ever intended for low-level, hence the clipped wings (they had a very damaging effect on the rate of climb and service ceiling.)
I've been reading the files on this "cropped clapped" business, and cropping the impeller blades was great at low-level, but dreadful at height; it was eventually recommended that cropping should be kept to the 50-series Merlin, and there was a 50M 55M, with just such a mod.
As you say, there was little point in tinkering with the XII, with a longer nose and extra radiator needed for a two-stage Griffon, so it was better to wait for the XIV 21.
A couple of notes about compression ratios and then the Merlin superchargers.
An example of changing the compression of an engine a little else can be found in the American Ranger six cylinder L-440 engine. At the end of it's life it was available in 4 versions.
A 25% increase in compression giving a 14.3% increase in power. A 25% increase in manifold pressure in an engine "should" give a 25% increase in power, minus what it takes to drive the supercharger.
Merlin's seem to have 5 or 6 different superchargers, not including different gear ratios or drives.
1. The supercharger used on the Merlin III and others including the 2 speed Merlin X.
2. The Hooker modified supercharger on the Merlin XX and 45. Also used on other marks.
2a. The same as above with a cropped impeller.
3. A modified supercharger using a larger impeller (10.85in vs 10.25in) with circular arc rotating guide vanes and a modified diffuser. This was good for several thousand more ft of altitude and used in the Merlin 46, 47, 50A and 56.
4. The famous two stage supercharger. Which required a strengthened drive for the higher pressures. It had an 11.5 in first stage rotor.
5. A modified two stage supercharger with a 12 in first stage impeller, modified guide vanes and a modified diffuser. It's first application was in the Merlin 65 but the two types overlapped some in MK numbers. Different gear ratios were used to adapt the supercharger/engine to different altitudes. A little used version was the Merlin 110-114A series which used the newer supercharger with the original gear ratios to give 1325hp at 27,250 ft with 18lbs of boost ( no ram?).