I agree with @wms7 that the Office of Combination Products (OCP) would review the primary mode of action (PMOA) to determine the agency assigned; CDRH, CDER, and CBER.

When looking at the additional OCP link @wms7 provided, I found that if OCP doesn’t have enough information to determine the PMOA of a product directly or cannot determine the PMOA with reasonable certainty, OCP will assign the combination product in accordance with the assignment algorithm at 21 CFR 3.4(b).

So What is the Assignment Algorithm? The Assignment Algorithm has 2 steps:

Step 1. If there are other combination products that present similar questions of safety and effectiveness with regard to the combination product as a whole, the Agency will assign the combination product to the Agency component that regulates those other combination products. See 21 CFR 3.4(b).

Step 2. Assign the combination product to the Agency component with the most expertise related to the most significant safety and effectiveness questions presented by the combination product. This would be used in cases for example, the RFD might present the first such combination product, or the combination product presented might differ in its intended use, design, formulation, such that it presents different safety and effectiveness questions than existing combination products.

Overall, the FDA gives clear guidance on how to write a Request for Designation and the FDA will provide a designation letter within 60 days.

https://www.fda.gov/RegulatoryInformation/Guidances/ucm126053.htm#IIIA