There are two mistakes here, bacteria can take up more than one plasmid of the same plasmid, the origin of replication will determine with the bacteria metabolism, how many copy numbers you yield. That means there are low copy origin and high copy origins.
If you talk about two different plasmids: if they have the same origin then they compete. Some origins are not compatible with each other at all. Others are. I have bacteria which have 3 different plasmids which have of course different selection markers too to keep them stable - but the selection of complementary origins is crucial in this case.
I agree with Abdelhalim, this is not a true statement. Every bacteria take up variable amounts of plasmid, which is why you get different yields back from your plasmid preps.
There are two mistakes here, bacteria can take up more than one plasmid of the same plasmid, the origin of replication will determine with the bacteria metabolism, how many copy numbers you yield. That means there are low copy origin and high copy origins.
If you talk about two different plasmids: if they have the same origin then they compete. Some origins are not compatible with each other at all. Others are. I have bacteria which have 3 different plasmids which have of course different selection markers too to keep them stable - but the selection of complementary origins is crucial in this case.
I'm with Ulrike and Adam, this is not the case. A bacterium can take up many (different) vectors at the same time. Of course there are a lot of caveats depending on the different types of plasmid you introduce, but there's no reason a bacterium can't uptake multiple different vectors into the one individual cell - that's one of the reasons why it's so important to sequence/validate your cloning/transformation experiments.
I agree with the others, this is just a compatiblity problem. Check the origin of replication of your plasmids, most likely they can't be propagated together in the same cell. Here's more info on this matter: http://www.bio.davidson.edu/courses/Molbio/Protocols/ORIs.html
The existance of the two different plasmid in single cell depends on plasmid incompatibility group. If two different plasmids have same incompatibility group then either of the two will exist in cell. This mechanism is used to remove large plasmid from the cell by introducing plasmid of same incompatibility group.
When we digest a large DNA molecule and than clone all fragments to one type of vector and then introduce them to a suspension of E. coli, each individual E. coli get only one plasmid. Hitherto above are true.
But when we clone our fragments into two types on compatible vectors and then introduce to E. coli simultaneously, each individual E. coli get only one plasmid again and we can not find any clone with both vectors.
But when we introduce our vectors to our bacteria in different step, they can get different plasmid. And when we use different selection markers, we can introduce and maintain incompatible vectors into our bacterium too.