The major evolutionary transition to multicellularity shifted the unit of selection from individual cells to multicellular organisms. Constituent cells must regulate their growth and cooperate to benefit the whole organism, even when such behaviors would have been maladaptive were they free living. Mutations that disrupt cellular cooperation can lead to various ailments, including physical deformities and cancer. Organisms therefore employ mechanisms to enforce cooperation, such as error correction, policing, and genetic robustness. We built a simulation to study this last mechanism under a range of evolutionary conditions. Specifically, we asked: How does genetic robustness against cellular cheating evolve in multicellular organisms? We focused on early multicellular organisms (with only one cell type) where cells must control their growth to avoid overwriting each other. In our model, unrestrained cells will outcompete restrained cells within an organism, but restrained cells alone will result in faster reproduction for the organism. Ultimately, we demonstrate a clear selective pressure for genetic robustness in multicellular organisms and show that this pressure increases with the total number of cells in the organism.