Can you target more than one gene in the same cell using the shRNA system if interested in co-silencing two target genes in the same cell?

The answer is yes, by two methods: 1. You could transduce with one type, select with puro and then transduce with the second type. Remember that after the second transduction puro selection will no longer be effective as the cells already have the marker from the first transduction. 2. You can simply mix the two virus types together and transfect at a high MOI and statistically get some cells with both types integrated. As with method 1, cells with either one or two types of virus will grow with puromycin selection so you will have to rely on statistics to ensure you have a large population with both virus types.