I had assumed that multiclassing let you qualify for anything that had a class as a requirement. I was looking at the rules again, though, and it only says that a character with a multiclass feat "counts as a member of that class for the purpose of meeting prerequisites for taking other feats and qualifying for paragon paths."
The section describing epic destinies says that "Epic destinies are broader in scope than a class or paragon path. Though most have certain requirements to enter, even these typically apply to a wide range of characters with various backgrounds, talents, and powers." That's true of 3 of the 4 epic destinies in the PHB, but Archmage and most of the epic destinies in the power books have a specific class (or classes) as a prerequisite. Since multiclassing doesn't let you satisfy that requirement, it looks like most epic destinies are actually more restrictive and harder to qualify for than paragon paths.
Have I missed any relevant rules text here?
The section describing epic destinies says that "Epic destinies are broader in scope than a class or paragon path. Though most have certain requirements to enter, even these typically apply to a wide range of characters with various backgrounds, talents, and powers." That's true of 3 of the 4 epic destinies in the PHB, but Archmage and most of the epic destinies in the power books have a specific class (or classes) as a prerequisite. Since multiclassing doesn't let you satisfy that requirement, it looks like most epic destinies are actually more restrictive and harder to qualify for than paragon paths.
Have I missed any relevant rules text here?