I have the answer directly from TWRA quota hunt team
When you select your hunts, you have the opportunity to select whether you want to enter "1" or "2" drawings. 2 is the max.
If you only select 1 drawing, then once you draw your choice you are done.
If you select 2, then once you draw your choice your priority points reset to 0 for the second quota drawing.
Every quota hunt has a "pool" that is made up of every person who put in for that hunt. It then creates a tier list by priority points per hunter and grants the awarded quota permit from the top down, then it's lottery once it gets down to a tier where there are more hunters with the same points than there are permits available.
It is possible to draw 2 hunts in the same year, just low odds because it just means you would have to have been drawn for a hunt with 0 points.