Alright lets see how I can plan this up. I believe that the deepest ice in Antartica is about four kilometers deep and well below sea level. I shall head a tiny bit more inland and begin to make it.
These should be the specifications:
Depth:There are two caverns, the first ice cavern which is four kilometers down, five miles wide and at it's highest point 1,000 meters below sea level. The second exists six miles below the first and is ten miles in diameter, and is three miles at it's highest point.
Supports:Both will naturally be supported by ice and rock but if Myself helps me then there can be a system of pillars imbued to make any structure stable in both caverns.
Cave network:Both will have a series of tunnels to caves at the ends of their perimeters. The caves are used for storage and will become factories of ability imbued replicators to make what we need.
If the ice melts in the flood:If the Global Flood melts all the ice then I lay claim to the land that exists under Antartica. It will likely be under the water but I will expand the first dome to cover it in a type of glass bubble to make an underwater city.
Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn