While moscafj's advice for gradually getting to the answer can be a good practical solution (you can add flour but you can't get it back out) it doesn't hurt to do the math first and see what to expect.
You have here 450 g liquid (including the eggs), and the flour is in the interval between 3 and 4 cups. At 120 g per cup, this means a baker's percentage of 94 to 125%, which is huge (most breads stay in the 60-80% range), and it doesn't even count the shortening, which softens the dough further.
You can start with gradually adding the flour as suggested, but you can also be brave and start with the 3 1/2 cups, and don't be weirded out if it turns out that you need more than 4 cups just so the dough will hold a little bit of shape. This assumes you are measuring in a roughly standard way (leveled cups, no packing). If you aren't, all bets are off, you might want to just use a scale, see how much it needs the first time (by feel) and then continue improving the recipe from there in subsequent batches.