GE and Boeing both operate a 747 for this purpose, the GENx engine for the 777x is the last I have heard of undergoing test flight.
Boeing has pretty much retired RA001 (the very first 747) - it now belongs to the Seattle Museum of Flight. Boeing now expects the engine companies to do the heavy lifting in testing new engines.
GE actually has two 747 test aircraft - one real early 747-100, and a newer 747-400 that they recently refurbished into a flying test bed.
One of the GE 747s is being used for the CFM LEAP engine (737 MAX/A320 NEO), the other will soon start flying with the GE9X engine for the 777X.