I have implemented NEB protocol for E. coli BL21(DE3) competent cells in order to transform two plasmid at the same time, but i just have transformed one plasmid in E. coli.
Yes, i have co-transformed two plasmid carrying different selection antibiotic markers in chemical competent E. coli BL21(DE3). You will need a combined antibiotic containing plate.
Usual Calcium chloride magnesium chloride protocol given in Molecular Cloning a laboratory manual, by Sambrook. 200 uL cells and 20 ng of each plasmid is sufficient.