The deepest caves that we know of are the Krubera Caves in Georgia (the country). These have been explored as far down as ~2200m deep. There are about 13km of explored tunnels, but none of the spaces are very large, nothing that would support a city.
The world's longest cave is the Mammoth Cave system in Kentucky (the state). These cover ~213 km$^2$ and have 652 km of surveyed cave tunnels.
The largest single cave room in the world is the Sarawak Chamber in Gua Nasib Bagus in Malaysia on the island of Borneo. This room is rougly 600m by 400m and has surface area of 0.16 km$^2$. That isn't super big, but could support a city of 10,000 or so with really packed conditions. There is an average of 58m of overhead in the Sarawak Chamber, so plenty of room for building up.
So those are the rough limits for a natural cave. With a little human architecture, and Roman-level engineering skills (aka the arch and concrete), it would probably be possible to make a series of rooms the size of the Sarawak Room covering an area the size of Mammoth caves. Think of them as neighborhoods of a few thousand people, each joined by short tunnels to the other part of the underground city.
As far as the catacombs go, 58 meters gives plenty of room for a lower level of ruined buildings, and an upper layer of active city or neighborhood on top of that. Since it is dark, there isn't really a lot of advantage in 'open sky' so no reason not to build to the ceiling.