yes it is possible. The best way to achieve this is providing that each of your plasmid has a selection marker you can easily follow (either a drug resistance cassette or a fluorescent reporter).
The amount of plasmids per se is not an issue, the only problem is that transfection/transduction with multiple vectors can lead to a poor percentage of cells correctly expressing all the plasmids for stochasticity reasons.
If you encounter difficulties in transfecting all 4 of them at once you can perform stepwise transduction (e.g. establish a stable cell line with plasmid 1, then transfect and select with plasmid 2 and so on.
However the approach you will choose will most likely depends on the cells you are studying. If they are highly transfectable you will not have any problem transfecting with 4 plasmids at once.
Yes it is possible, but as Francesco mentioned the probability of all the plasmids getting into a single cell is very less. I had been working with three plasmids, it was very had to screen it. Care has to be taken to see that all the plasmids have different antibiotic resistance, or else screening is very very difficult. The other way is to do it one by one, if you have more time and even in this case it would be wise to have different antibiotic resistance