The area that would be most relevant would be "operational control."
This is the concept that the operator, or certificate holder, must have operational control over the aircraft, the crew, and the flights. A necessary rule to combat operators who historically were renting out their certificate to just about anybody who then flew around as an air carrier while the actual certificate holder was oblivious to what was happening on a day to day basis. It's still possible to rent out space on your certificate but the holder must maintain "operational control" on the day to day operations as if it was their own aircraft.
The operator can also still broker out sales of seats and charters to a third party who is not an operator but that third party may not represent themselves as an airline or operator in any way. They can act more like a travel agency but in an exclusive (or mostly exclusive) arrangement. The actual operator must be clearly identified to the passenger by the approved business name or DBA on their operating certificate. There are ways to make it work without running afoul of this requirement.
The advantages of such an arrangement are the ability to isolate yourself from the liability of the operator and even to seamlessly switch to a new operator on a semi or permanent basis as needed to meet the needs of your customers. It also allows you to manage expenses more efficiently so you can assure unforeseen events will be less likely to impact profits.
The disadvantages are that unless you have a really good relationship with the operator you may have issues in getting the service you require and the reliability you need. You are also at the mercy of their ability to make a profit from the arrangement or they may decide to back out of the arrangement at any time. These are difficulties that can be overcome through a solid business relationship.
In other words, yes it's possible to have an arrangement like this but it must be tailored to fit within the confines of these rules. The exact details of such an arrangement should be crafted with the help of a qualified aviation attorney experienced in such matters (not a litigator who chases airport firetrucks). After that it should be reviewed by another qualified aviation attorney and run by the local FSDO office and the operator's POI.