You can put multiple firearms on a Form 4473. A dealer sold me 4 Anderson lowers and did it all on one form. Your local FFL shouldn't charge per firearm, just a one time fee. If they do, find someone else.
Bingo. My LGS/FFL will let me transfer as many as I want on one Form 4473, if done at the same time and I don't go crazy with it. $10 transfer fee, $5 background check. If your FFL isn't doing something like that for you, you need to look for another one.