For a sub with Italian style cold cuts, order it with double cheese (provolone) and tell them to hold the mayo and mustard. In addition to the meat and cheese the sub needs lettuce, tomato, and onions, and just a little pickled red pepper if they have it. Ask for a little red wine vinegar and good olive oil on both pieces of bread before the filling is put in place, and more of the same plus oregano and black pepper on the lettuce before the sandwich is closed.
Something else you want is more copa and less sliced ham, if they will do it that way, to avoid ending up with ham sandwich flavor, no matter if it has salami and so on.
If they don't have decent vinegar and oil, at least think about taking it home and adding those items there. You don't really want soy oil, etc.
Make sure you get extra napkins.
I came up with this application of dressing items - vinegar and oil on the bread - on my own but one day the man making the sandwich just smiled and asked if I was from Jersey. Seems he had a lot of customers who asked for that combination before he left home. He had a name for it, which I've forgotten.
There is a happy point with a sandwich made this way where the bread is not soggy but no question that the vinegar and oil add to every bite.