The authors explore the $R$Te${}_{3}$ family of materials as a clean model system in which to study a quantum phase transition between single and double charge density wave states. Quantum oscillation measurements reveal a significant reduction in the area of the Fermi surface across the quantum phase transition, but no obvious divergence of the electronic effective mass. Variation of the magnitude of the charge density wave gap across the rare-earth series leads to a particularly clear example of tunable magnetic breakdown.