Catastrophic is taken to mean meters of sea level in a few hundred years or less. Sea ice cannot change sea level much. That is can do so at all is because sea ice is not made of quite the same material as the ocean. So the meltwater still 'stands' a little higher than the local sea level. Not a large figure, but not zero either.
Mountain glaciers appear to have already made their contribution.
The three ice sheets can change sea level significantly, depending on whether they grow or decay. They are grounded on land. Sometimes, which will be important in a minute, that land is far below sea level. As with bank accounts, it is income minus outgo. It is believed that in a warmer climate, the amount of precipitation would increase.