Inheritance of 5-methyl cytosine modification of CpG (CG/CG) DNA sequences is needed to maintain early developmental decisions in vertebrates. The standard inheritance model treats CpGs as independent, with methylated CpGs maintained by efficient methylation of hemimethylated CpGs produced after DNA replication, and unmethylated CpGs maintained by an absence of de novo methylation. By stochastic simulations of CpG islands over multiple cell cycles and systematic sampling of reaction parameters, we show that the standard model is inconsistent with many experimental observations. In contrast, dynamic collaboration between CpGs can provide strong error-tolerant somatic inheritance of both hypermethylated and hypomethylated states of a cluster of CpGs, reproducing observed stable bimodal methylation patterns. Known recruitment of methylating enzymes by methylated CpGs could provide the necessary collaboration, but we predict that recruitment of demethylating enzymes by unmethylated CpGs strengthens inheritance and allows CpG islands to remain hypomethylated within a sea of hypermethylation.