Engine mfgrs. generally have testbed aircraft flown by test pilots. Some a/c I can recall over the years - XF4D, B-17, B-47, B-52, VC-10, AJ-1, 720, 727-100, MD-80, 747, Gulfstream I, ... (This list includes aircraft flown by RR, GE, P&W, Avco etc.)
Generally used for engine development work. This can include airstart tests, envelope expansion, High AOA, crosswind, everything required to minimize the surprises when the engine enters service.