As tfung and Markie say, it's easy and very possible.

After deplaning, I suggest that you just go back to the same gate. You need to clear security before getting back to the same gate. The departure and arrival floors are the same just like Changi in SIN. At the gate, they can issue you a boarding pass. If you have time, you can then go to the lounge. I don't know if they would issue a boarding pass at the lounge, though. Does anyone know?

I would not go to the transit counter. I've never seen people from CX.