While your query can better be addressed on Cruise Critic I might also be able to help.
We have sailed on the Connie and her three sisters.
What class cabin did you book? When is your cruise? Did you book with a travel agent or through Celebrity?
Generically, paid upgrades are difficult to come by on the majority of sailings. Free upgrades are an even more illusive goal. The best way to upgrade is always done before you sail.
If you want to give it a try once onboard check in at the Purser's desk. There will almost always be a sign that indicates the ship is full but talk to the staff. They will, no doubt, tell you to check back after the ships sets sail. If there is an available cabin they probably won't know until after the CPB forms are filed and then they are busy with sail away.
If you booked with any promotions be aware that they could be lost in altering your booking. On July 5th the promotions changed and this could affect any change request.
I will check your thread tomorrow to see if I can be of any additional assistance. I am not a travel agent but very experienced cruiser.