Trademarking an LLC name that acts as a parent company for multiple brands

I'm working with a trademark service and we've hit a point where I'm not sure if I'm misunderstanding the process or if what I'm trying to do just isn't a typical use case.

I have several brands that operate in different product categories, and each brand either already has its own trademark or will eventually have one filed under the appropriate class for the goods or services it offers.

Instead of creating a separate LLC for each brand, I formed a single LLC that owns and manages all of them. The LLC itself isn't consumer-facing. Customers would only see the individual brand names on products, websites, packaging, and marketing materials.

I wanted to trademark the LLC name and logo as well, mostly because it serves as the umbrella company behind these brands. However, the trademark service keeps asking me what goods or services the LLC provides so they can determine the appropriate class, and they don't seem satisfied with my explanations.

My thought process was that the LLC functions more as a holding or management company overseeing multiple brands. I wondered whether something related to business management or retail services might apply, but I'm starting to question whether I'm trying to trademark something that doesn't fit neatly into the standard trademark framework.

Has anyone successfully trademarked the name of a parent company or holding LLC that doesn't directly sell products under that name? If so, how did you determine the correct trademark class and demonstrate actual use in commerce? Or is it generally unnecessary to trademark the LLC name if the individual brands themselves are already protected?