In simple terms, the Air Carrier Certificate does not state any limitations. However, the Air Carrier's Operations Specifications will
State whether they are:
Domestic 121
Flag 121
Supplemental 121
On Demand 135 Single Pilot
On Demand 135 Single PIC
On Demand 135 Air Ambulance
Etc etc...
A certificate holder can request amending their OpSpecs anytime by following a process specified in the regulations. A certificate holder can shrink, grow, and change their operation. The DOT and FAA will assess whether the certificate holder is fit, willing, and able to perform the requested operations before signing and issuing the OpSpcs. See FAA Order 8900.1, Volume 3 for the Air Carrier Certification Process.