Alkali doping and alloying are well-known strategies to improve the performance of Cu2ZnSn(S,Se)4 (CZTSSe) absorber based thin film solar cells. The effects of individual light alkali elements such as Li and Na have been thoroughly investigated, with both dopants resulting in significant improvements in performance of CZTSSe solar cells. Here, the combined effects of Li and Na are investigated in a so-called co-doping approach to capture the benefits from both elements simultaneously. In order to do that, various concentrations of Li and Na between 0.0 M and 0.5 M are added to the solution used for spin coating of the precursor layer. After annealing under Se-enriched atmosphere, the two alkali elements displayed mutual dependency of in terms of their concentrations in the CZTSSe absorber layer. Furthermore, both, Li and Na showed signs of forming alloys with the CZTSSe phase. The efficiencies of the best Li-Na co-doped solar cells are above 10%, slightly above the Li baseline thanks to increased open-circuit-voltage and short-circuit current. A non-negligible Na incorporation was observed even in nominally Na-free devices, likely from indirect contamination from the SLG substrate. Further work is needed to better understand Na-poor compositions and draw conclusions relevant to Na-free substrates.