We are currently incorporated and "doing business as" a registered name. Can we add an additional "brand" to operate a separate business function?

For example we are incorporated as Thomas & Sons llc, dba Perfect Plumbing. We''d like to also do HVAC, but don''t want to use the plumbing moniker. The HVAC service would more or less operate as a separate business function. Different branding, site, etc. Ideally this would still all be under Thomas & Sons llc. Is this possible or do we need to set up a new corporation for the HVAC part of the business. Also, when it come to the most important part of payment. How would we bill? The new HVAC name, Thomas & Sons llc or the DBA name. I''d like to keep things as simple as possible for the customer while sill maintaining the identity of each business unit. Thanks for your help.