It has recently been proposed that mobile elements may be a significant driver of cooperation in microorganisms. This may drive a potential conflict, where cooperative genes are transmitted independently of the rest of the genome, resulting in scenarios where horizontally spread cooperative genes are favored, whereas a chromosomal equivalent would not be. This can lead to the whole genome being exploited by surrounding noncooperative individuals. Given that there are costs associated with mobile elements themselves, infection with a plasmid carrying a cooperative trait may lead to a significant conflict within the host genome. Here, we model the mechanisms that allow the host to resolve this conflict, either by exhibiting complete resistance to the mobile element or by controlling its gene expression via a chromosomally based suppressor. We find that the gene suppression mechanism will be more stable than full resistance, implying that suppressing the expression of costly genes within a cell is preferable to preventing the acquisition of the mobile element, for the resolution of conflict within a genome.