You can. I did three time already without quit my old job first. Because if you get rejected, you still can use old one enter US
-boringcrazy(boringcrazy);
2006-9-22(#3221713@0)
Without expiring the current TN, you can apply new TN and tell the US custom official that you'd like to expire the current TN and would like to apply a new one at the border.
-stevenwang(Steven Wang);
2006-9-22(#3221739@0)