Originally Posted by
Ready2Go
A TA also once explained to me that their computers can't handle a request to check a bag on to a flight that is not the next instance of that flight number. So, for instance, if there's a QF94 LAX-MEL departing in 5 hours and another departing the next day (29 hours), the computer can't understand that you want the one in 29 hours. (I have no independent knowledge as to whether this is true, but this TA seemed quite knowledgeable.)
I've managed to get the computer to do that, so I wouldn't say it's impossible. Just highly inadvisable.
I would suggest looking into a baggage storage service at TPA rather than increasing the odds of your bags being mishandled by leaving them in the system all night.