Performing censuses on stigmatized or vulnerable populations is challenging, however, for such populations partial enumeration is often possible using different lists or sources. If the sources overlap then multiple systems estimation (MSE) methods can be applied to obtain an estimate of the total population. These are typically expressed by a log-linear model which permits positive/negative dependencies between lists. This paper considers issues that arise for the application of MSE to modern slavery where there is little to no overlap of individuals across lists. We investigate the robustness of MSE in terms of the importance of each list and the impact of combining lists on the estimation process. We undertake a simulation study and consider real national modern slavery data from the UK and Romania.