Yes, they can. If the plasmids are very different and have different oris then they might be able to coexist, if they have the same ori then the copy number will most likely be reduced for both of them. The selection must be applied to both for them to coexist, otherwise, the unselected one will be lost eventually. Although it might be able to co-exist inside cells carrying the other plasmid conferring resistance for a while.
When you transform your plasmids to bacteria multiple are taken up, if the plasmid solution is pure and contains a single plasmid then double transformants will not be a problem. However, some experiments will make the transformed solution have two or more plasmids, like ligations (undigested, re-circularised and cloned construct). With ligations, I have not had problems before, but there are other techniques in which double transformants are inherent to the experiment.
The solution is very simple, extract the plasmids from the colony you think has 2 plasmids and transform it again to bacteria at very low concentrations (0.1 or 0.01ng/ul will do).
Bruno Salomone Gonzalez de Castejon gave an excellent answer, there are many instances of multiple plasmids in a bacterium, even with natural plasmids in populations from the wild.