We study electronic transitions in highly charged Cf ions that are within the frequency range of optical lasers and have very high sensitivity to potential variations in the fine-structure constant, α. The transitions are in the optical range despite the large ionization energies because they lie on the level crossing of the 5f and 6p valence orbitals in the thallium isoelectronic sequence. Cf(16+) is a particularly rich ion, having several narrow lines with properties that minimize certain systematic effects. Cf(16+) has very large nuclear charge and large ionization energy, resulting in the largest α sensitivity seen in atomic systems. The lines include positive and negative shifters.