Dielectronic recombination (DR) rate coefficients for 22 sodium-like ions, between Mg+ and Xe43+, forming magnesium-like ions have been calculated as part of the assembly of a level-resolved DR database necessary for modelling dynamic finite-density plasmas, within the generalized collisional - radiative framework. Calculations have been performed from both ground and metastable initial states, in both LS - and intermediate coupling, allowing for Delta n = 0 and Delta n = 1 core-excitations from ground and metastable levels. Partial and total DR coefficients have been calculated for Mg+ to Zn19+, as well as Kr25+, Mo31+, and Xe43+. Results for a selection of ions from the sequence are discussed in the paper and compared with existing theoretical and experimental results. A full set of results can be accessed from the Atomic Data and Analysis Structure (ADAS) database or from the Oak Ridge Controlled Fusion Atomic Data Center (http:// www-cfadc.phy.ornl.gov/data_and_codes).