A useful little quirk about the 747 is that it can ferry a fifth engine on the wing, for when another aircraft is stranded somewhere in the world.
One of the main reasons the 747 was given the ability to ferry an engine was due to the lack of large cargo aircraft available at the time.
Don't forget the 747 was a major game changer when it came out, it was designed to replace the 707/DC-8, and was almost twice the size of these aircraft. As a result, there just wasn't anything available to transport a 747 engine by air if needed.
This was a major problem that had the potential to affect sales of the aircraft, and so they had to find a solution to this. It wasn't until the 747 began to be introduced as a cargo carrier that it was possible to transport these engines by air, in the hold of an aircraft.
With the introduction of the A380, there was no need to add engine ferry capabilities, as large cargo aircraft were common enough to transport them.
The A380 does not appear to have the capability to transport an extra engine under the wing. Higher engine reliability combined with widespread availability of air cargo transport makes this option redundant in modern jets.
*Trent 900 can be transported in a 747-400F without disassembling. For Engine Alliance GP7000, you'll need an An-124.