Spitfire vs Spitfire?

This is a 1/72 model of a Mk V Spitfire.

The Danish pilot of the actual aircraft, Aksel Svendsen, was killed in a dogfight on April 24, 1942, and, as far as I can tell, this is a contemporary photo of the aircraft my model is based on.

Occasionally, aircraft ended up in enemy hands, and I got my hands on a model of a Mk I Spitfire, in Luftwaffe 'colours'. 

The aircraft this model is based on was shot down by a Messerschmitt Bf109 in France, and its pilot, Richard Hardy, was taken prisoner. I managed to find a contemporary picture of the actual aircraft on the ground, still with RAF roundels, guarded by German soldiers. 

Subsequently, the damage to the aircraft was repaired and it was painted over; there is a bit more here. Also, there is an entry in the 'Spitfire International' book, which I got recently:

So .... were there ever Spitfire against Spitfire dogfights in WW II?

As far as I've been able to ascertain, there have never been any Spitfire-Spitfire dogfights in earnest in Europe, so the Luftwaffe Spitfire was never in combat with RAF Spitfires.

The one time that Spitfires were in combat with Spitfires was in the Israel-Arab war of 1948; watch this space ...