We studied the persistent luminescence in europium-doped calcium thiosilicate upon codoping with the rare-earth elements neodymium, dysprosium, samarium, and thulium. The strongest afterglow was observed for neodymium codoping. The persistence emission spectrum is dominated by a band at 660 nm, which makes the afterglow color redshifted compared to the steady-state luminescence. Thermoluminescence measurements revealed different glow curves for the two europium lattice sites in the Ca2SiS4 host, suggesting that transfer of charge carriers via the conduction band is of minor importance. Finally, we conclude that the Nd3+ ions occupy lattice sites in close proximity of the Eu2+ ions, based on site-selective luminescence measurements on Ca2SiS4:Eu,Nd.