No. You are only able to enroll in one Medicare Part D plan at a time - joining a second Medicare plan will automatically disenroll you from your previous plan.
If you spend your time between two states (two states that are not in the same
Medicare Part D Region), you would purchase a Medicare Part D plan in the state where you have your closest contacts - such as: primary residence (the address used for filing taxes), Driver's License, and pay state taxes.
The good news is that your chosen Medicare Part D plan (no matter where it was purchased) can be used at any of 50,000 to 60,000+ pharmacies across the country. In short, no matter where your primary residence, you should have no problem filling your prescriptions in New Jersey, Florida, or any other state.