No. A licensee must initiate a new NICS background check for each completed firearms transaction. However, a person may purchase or acquire several firearms in one transaction.
[27 CFR 478.102]
Example: A transferee completes an ATF Form 4473 for a single firearm on February 15. The licensee receives a “proceed” from NICS that day. The licensee signs the form, and the firearm is transferred. On February 20, the transferee returns to the licensee’s premises and wishes to acquire a second firearm. The acquisition of the second firearm is a separate transaction. Therefore, a new NICS check must be initiated by the licensee.
Example: A transferee completes ATF Form 4473 for a single firearm on February 15. The licensee receives a “proceed” from NICS that day. The transferee does not return to pick up the firearm until February 20. Before the licensee completes the transfer of the first firearm, the transferee decides to acquire an additional firearm. The second firearm may be recorded on the same Form 4473. The acquisition of the 2 firearms is considered a single transaction. Therefore, the licensee is not required to conduct a new NICS check prior to transferring the second firearm.