I grind once. The reason I do is to maintain the integrity of the meat. Meaning, when you take a chunk of meat and grind it thru a plate, you have now made a large piece into a small piece. And when you run it thru again, you take a small piece and make it even smaller. Some recipes and styles of sausage call for that however, but most don't.
Some will grind and then add their spices and such to the mix and then grind again. You can get around this and it works very very well. Say your going to grind a pork butt into some sausage. Cut the meat into strips, I go 3/4" x 3/4" by however long the piece comes out. Some will go 1" x 1", but I would not go larger than that. Now you have a tub of cut pork strips. Add your spices and such to this and let it sit for a few hours under refrigeration so things can mix up and absorb. Before grinding, make sure that these meat pieces are very very cold, somewhat frozen but still pliable. Run the seasoned meat thru the grinder and out comes ground, seasoned meat. Next step is to stuff. Make sense? Some grinders will even allow you to run your stuffing tube off the end and do everything in one shot. Grind the seasoned meat and it goes right into the stuffing tube and into your casings. By running it thru once, and ensuring that the meat is almost frozen, your grinder will do what it was designed for, grind, and a nice sausage will reflect that as the meat will look individual pieces inside the casing and not a meat paste.
If you cut your meat into small strips, you will have no problem running it thru once on a 3/16 plate. Just make sure to let the auger take the meat on its own and not force it. That will give you some mushy meat.