Messerschmitt P.1091

The Messerschmitt P.1091 was a series of projects to convert a regular Bf.109G into a high altitude fighter.
The project began in May 1942 when the Reich's Air Ministry announced the need for a new high altitude fighter which should be operational for late 1944, in order to counter the threat of the American B-29 bomber, which thanks to its high service ceiling, was out of reach of German fighters.
Messerschmitt offered a design based on the Bf.109H (a high altitude variant of the regular Bf.109), called P.1091. The design was, in fact, a stretched version of the 109 where the wings and the rear fuselage were enlarged.
The P.1091 Stuffe I (Stage I) was to quickly produce an aircraft that could reach theoretical altitudes of 17.000 m high (55.750 ft). The Stuffe I was to be powered by a modified turbocharged Daimler Benz DB 605 and armed with three 20mm MG 151 cannons.
By July 1943 it was thought that a higher operational fighter would be necessary, so the P.1091 Stuffe II was proposed to be powered by a Daimler Benz DB 628 high altitude engine with a pressurized cockpit, however, as shortly later, in August 1943, design work on the Stuffe III began.
The Stuffe III's design was similar to the Stuffe I's one but powered by the DB 603U engine or the DB 632. The DB 632 was a modified DB 603 to drive two contra-rotating four-bladed propellers.
As it was obvious that the designs couldn't be materialised within a reasonable amount of time, the RLM transferred every design work to Blohm & Voss, however, Messerschmitt continued work on a high altitude fighter, this time based on the Me.209.
Apparently, to test the DB 628 engine, a mock-up of the engine installation was made in a Bf.109G V49, which was based on a Bf.109G-5. The DB 628 was flight-tested in the Bf.109 V-50 and V-54. After the tests with the V-54, Messerschmitt abandoned every project with the DB 628 engine and the P.1091 was definitely cancelled in mid 1944.

Sources:
1. http://me109.airwar1946.nl/family/1091.htm
2. Midland Publishing - Luftwaffe Secret Projects - Fighters 1939-45
3. AJ Press - Monografie Lotnicze 44 - Messerchmitt Bf.109 Cz.3 (translated)