The Maximality Principle $\mathrm{MP_{CCC}}$ is a scheme which states that if a sentence of the language of ZFC is
true in some CCC forcing extension $V^\mathbb{P}$ , and remains true in any further CCC-forcing extension of $V^\mathbb{P}$ , then it is true in all CCC-forcing extensions of V, including
V itself. A parameterized form of this principle, $\mathrm{MP_{CCC}}(\mathbb{R})$ , makes this assertion for formulas taking real parameters. In this
paper, we show that $\mathrm{MP_{CCC}}(\mathbb{R})$ has the same consistency strength as ZFC, solving an open problem of
Hamkins. We extend this result further to parameter sets larger than .