If I understand the question correctly, you have oral HSV-1 and are wondering if it's possible to subsequently contract oral HSV-2? I don't think this is possible. Any newly introduced HSV-2 is going to be 'out competed' by your existing HSV-1 orally. It's HSV-1's home turf, so to speak.
Let's see what the experts think.
This is a very good question. I posted something to this a few days ago. I am not sure if u can get type 2 on your mouth if u already have type 1.