Carbon-enhanced metal-poor (CEMPs+r) stars show large enhancements of elements produced both by the slow and the rapid neutron capture processes (the s and r process, respectively) and represent a relatively large fraction, 30% to 50%, of the CEMP population. Many scenarios have been proposed to explain this peculiar chemical composition and most of them involve a binary companion producing the s-process elements during its Asymptotic Giant Branch (AGB) phase. The problem is that none of the proposed explanations appears to be able to account for all observational constraints, hence, alternatives are needed to be put forward and investigated. In this spirit, we propose a new scenario for the formation of CEMPs+r stars based on S. W. Campbell's finding that during the ‘dual core flash’ in low-mass stars of extremely low metallicity, when protons are ingested in the He-flash convective zone, a ‘neutron superburst’ is produced. Further calculations are needed to verify if this neutron superburst could make the r-process component observed in CEMPs+r, as well as their Fe abundances. The s-process component would then be produced during the following AGB phase.