I too have three original bring back Certificates. The reason for three in my case? Not 100% certain but I believe the reason why is the conditions/terms changed to allow for concealed weapons like pistols. (If someone has a better explanation, love to hear it.) See image.
The two original June 25, 1945 Certificates (#1 & #2) forbid concealed firearms. See Section 2. The single original June 27, 1945 Certificate does not. My guess there was a #4 which was turned over to the Army. He sailed home on the Queen Elizabeth in mid-July 1945. And Dad kept the older copies for prosperity.
In review, the purpose of bring-back papers was not to count or inventory GI trophies or to learn who had what. The primary purpose was to identify if such trophies were prototypes or rare examples of technical interest to the US Army. Examples like the Sturmgewehr 45(M), a Krummlauf attachment or an MG 45. The Walther P-38 and Luger 1917 Artillery do not fall into this category. Another purpose was safety, explosives contained in the trophies was prohibited. The format and conditions of within bring back certificates changed over time. Even in the same time period, their terms could vary from outfit to outfit.