Can two plasmids with the same origin of replication (for example pBR322 ori) and thus from the same incompatibility group be successfully co-transformed in E. coli? What are the mechanisms that would prevent the two plasmids from co-existing together? Does it matter what is the dual resistance selection? How would the efficiency of co-transformation compare to the efficiency of a uni-transformation?
It turns out that there doesn't seem to be a specific mechanism to prevent multiple incompatible plasmids from coexisting. Velappan et al put in more than one incompatible plasmid with different selection genes in them and put the bacteria on a single antibiotic and periodically checked for the second vector (by testing for second antibiotic resistance). It apparently took weeks for the second vector to disappear - many generations.
Higher copy number plasmids did better, with longer times to lose the second plasmid. They seem to conclude that its just the natural rate of loss of plasmids that will cause the bacteria to lose the second plasmid without selection. I imagine with two antibiotics in the culture it would take some months and you could potentially store the bacteria at -80C indefinitely. Still in most experiments its going to be an additional headache where compatible origins of replication seem to have a more typical half life for retaining the plasmids.
They also state that the frequency of double transformations is more frequent than is usually appreciated, which seems to imply that you will get some colonies from a typical high efficiency transformation from plasmid preps. However, they introduced the multiple plasmids by phagemid infection rather than transformation in this study.