According to 383.71, drivers must transfer their CDL within 30 days of moving. Each driver must obtain a CDL license from the state of domicile. That’s where the driver receives mail, has a permanent and principal residence, and is where the driver has the intention of returning whenever absent.
The regulations also specify that a driver can only hold one single driver’s license at a time per 383.21. The only time that a driver may hold two licenses is for a 10-day period after obtaining a new one.