We propose a new broadband search strategy for ultralight axion dark matter that interacts with electromagnetism. An oscillating axion field induces transitions between two quasi-degenerate resonant modes of a superconducting cavity. In two broadband runs optimized for high and low masses, this setup can probe unexplored parameter space for axion-like particles covering fifteen orders of magnitude in mass, including astrophysically long-ranged fuzzy dark matter.