The newly developed multiple mapping conditioning (MMC) approach for turbulent non-premixed combustion is applied to a series of flames with varying levels of extinction and reignition. This is one of the first applications of MMC to reacting flows and results for mixture fraction, normalised temperature and reactive species are compared with DNS data. MMC is a generalised approach applying mapping closure to a prescribed reference space. The dimensions of the reference space are problem specific; here reference spaces with a single mixture-fraction-like variable and up to three dissipation-like variables are used. The results for two flame cases show an improvement in accuracy over those obtained from conditional moment closure singly conditioned on mixture fraction or doubly conditioned on mixture fraction and scalar dissipation. Results for another case suggest that the essential physics of the problem may not be fully described by this modelling.