Usually one has to turn in or exchange their previous state's license for a new license when they move to a new state. Most states do not allow a person to hold a driver's license from more than one state at a time, however state laws differ.
If you have permanent residence in Massachusetts and only like part time in Florida then you should be able to hold onto your MA driver's license even when you are residing in FL.
Massachusetts RMV notes about converting over out of state licenses that all driver's license applicants who convert a license from another jurisdiction must surrender that license in order to receive a Massachusetts license.
Florida Statute (FS) Section 322.03(1)(B) states that a person who does not drive a commercial motor vehicle is not required to surrender a license issued by another jurisdiction, upon a showing to the department that such license is necessary because of employment or part-time residence.
This F.S. goes on to say that any person who retains a driver's license because of employment or part-time residence shall, upon qualifying for a license in this state, be issued a driver's license which shall be valid within this state only. All surrendered licenses may be returned by the department to the issuing jurisdiction together with information that the licensee is now licensed in a new jurisdiction or may be destroyed by the department, which shall notify the issuing jurisdiction of such destruction. A person may not have more than one valid Florida driver's license at any time.
So from the language of this Florida law it appears that you may be able to get a Florida license without surrendering your out of state license. To see if this is possible in your situation contact the Florida Department of Highway and Safety (HSMV).
Also keep in mind though that the FL HSMV states that any person who has a vehicle in Florida for more than 90 days during a 365-day period must purchase personal injury protection (PIP) and property damage (PD) liability insurance coverage. The 90 days do not have to be consecutive.