The firearms sale tracking information in the US system is incredibly distributed, and the 3310.4 represents one of the only forms that could be construed as a "registration" in so far as it aggregates any information whatever. Outside of that one piece of paper, the actual means of tracing a sale--much less multiple sales--is quite tedious, and involves faxed requests revolving around the 4473 which are made to the ATF, then followed through at NTC, then back to the ATF, then to the FFL, then back to the ATF, then back to the requester. And each of these steps requires a 1980s era fax machine and a time consuming / absurd search for actual physical documents in whatever filing cabinet or box. There is a documentary about NTC where workers there describe how the concrete flooring at the facility is buckling under the weight of the stacked up boxes of forms, specifically due to legislation that prevents the digitization of such data into any form of searchable database whatever. The entire process takes weeks.
Individual states may have additional reporting requirements, and those laws could include the filing of paperwork at the state level in parallel with the ATF. Were that the case, an investigator could indeed perform such a lookup with a bit more ease than trying to dig through the endless files at the NTC or by making educated guesses based on other investigative work. While I am not an ATF agent, I have spent many man hours trying to find the owner of various firearms, and this took all the steps mentioned above, and involved several long conversations with a few ATF special agents. I have been in the position of being quite curious what the total number of firearms purchased by an individual--in this case a wanted felon, likely a murderer, and known carjacker/bank robber--in a given state, much less any state in the Union, and was confounded by a process so byzantine and absurd that it boggled the mind.
In the case of an investigation, any one of those forms (3310.4 or 4473) would lead agents/officers back to the FFL from whom the weapon(s) were purchased. From there, if that FFL is your main squeeze, compiling a list of weapons that you've purchased is actually quite easy. This is one of the reasons why peer-to-peer sales are such a sticking point, legislatively. They not only skip the background check process, but they also fail to produce what limited paper trail there is regarding the purchase, transfer, and implied ownership of a firearm.
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