Hi Steve and Karen,
Yes, you can sometimes purchase on upgrade once onboard, but it depends totally on availability. First thing you want to do is ask as you are being processed at the port for check-in. Sometimes there are upgrades available dockside. If that doesn't work, you need to arrive onboard as early as possible, head immediately to the guest relations desk and ask. If the ship is sailing full and there are no upgrades available, there will usually be a sign posted at Guest Relations indicating same. Sometimes upgrades are available on the spot, sometimes they will place you on a "waitlist" (listed on a first come-first served basis). Then, if there are last minute cancellations that open space - you will be notified. It's worth a shot, but there are obviously no guarantees.