Don't think that can work. As you know, the Rapid Refill mugs have a chip in bottom that the soft drink dispenser reads and knows your check out date. When you purchase they are activated for "length of stay" for your room and expire at midnight the day you check out.
Anytime you check out and check back in, even if at the same resort, same room and on consecutive days, you'll have to purchase a new mug to use and have activated for 2nd reservation. Might be able to have old mug activated instead, but doubt it. When you buy the service for refillable beverages the mug is a part of the deal so you'll get a new one anyway and both cannot be active on the same reservation. Even if its lost. Lose one and they won't replace with a 2nd that's active unless you buy the privilege again.
Multiple MBs yes. Multiple mugs for same guest, no.