I'm designing a city where there are multiple layers of tunnels- there are catacombs(because the nobles ruling there bury their dead underground), there are escape tunnels from the royal palace, & there is a drainage system underneath all this. Is it possible to have all this underneath a city, specially in a world which is as technologically advanced as medieval Europe?
Of course you could have it. As a thought experiment, consider tunnels in a mountain: They can exist, and persist, with half a mile of rock and dirt above them. A mountain can be riddled with twenty stories of tunnels. There is little difference, the "overload" or weight of the Earth is not a big issue.
Likewise, we have mines on Earth that go nearly a mile deep, and not just straight down, they have many levels following many veins of the minerals they seek.
An issue that needs to be addressed is ventilation and ventilation shafts; I'm not sure exactly what is necessary or how it works, but I do know deep mines require them at regular intervals or they can become oxygen depleted, and/or toxic gases will accumulate.
As a writer you don't have to really know how they work either, unless you want them to be part of the plot: You can just have a character figure out what one of the shafts is for. Then never worry about it again! That proves they exist and it is plausible the tunnel engineers provided for ventilation so the audience can suspend any disbelief about the extent and usability of your underground setting
If the rock and the water table cooperate, wells and horizontal tunnels can be hundreds of meters deep and tens of kilometers long. Many of these qanats were built thousands of years ago, using iron-age technology.
The latter claims that: This Qanat is 33 km long, which consists of two original branches known as Qasabe and Doolaab, which it consists of 427 deep wells. Digging such a huge tunnel with the master well of 340 m deep and over 73 million m$^3$ excavation in 300 m deep....
- You might drop a remark about cave-ins and building collapses. The new guild hall had replaced the old one, which had vanished in a sinkhole 60 years ago. I wonder when people will stop calling it "new."
- In addition to catacombs, there might be storage cellars. Wine, beer, gold, ...
- What is the likelihood that an escape tunnel will lead into the sewer, or vice versa?
Just don't build your palace on marshy ground.
Qanats are deep, but below the water table
Catalyst's qanat links show how deep you can get, but those tunnels are actually wells; specifically designed to go below the water table, and thus full of water. This isn't necessarily a useful feature for your catacombs.
The water table is the normal limit...
Otherwise, you are limited by the water table, as other answers indicate. The water table is highly variable depending on your location, but it can't be too low, or else the people of your city won't be able to get well water. I doubt with a medieval tech level a large city would be sustainable in some palace with a water table over 100m due to the difficulty in obtaining fresh water. Of course, there could be a river nearby, but that much flowing water would seep into the bedrock and cause the water table to rise...
...unless you are constantly pumping water out
The Roman mines at Rio Tinto went down 137m and were around 80m below the water table. How did they keep the tunnels from flooding? By force pumping water out with complex wheel driven screws. Over 30 wheels were found in the mine complex, including a set of 16 wheels in pairs on eight levels, which pumped the water up out of the deepest parts of the mine, level by level, to an adit.
An adit is basically a qanat, except instead of going below the water level to provide irrigation to somewhere downhill, it goes above the water level, and water pumped from the mine depths runs downhill out of the mine complex. These adits sound like the drainage system you mention, although this one could go over the catacombs, not below it, and it could be used to drain water into reservoirs to feel wells in the city above.
These mines were operated in Roman times continuously for centuries. How did they stay water free for so long? Centuries of slaves, treading the wheels, pumping water out.
Provided the correct motivations (as in, Egyptian Pharaoh style motivations), a royal catacombs could be dug deep and maintained for centuries, maybe even across dynasties, by the ceaseless labor of slaves. Or, I mean, you could use donkeys too, but who would work a poor donkey underground like that?
It is all about the rock. The Roman catacombs were carved from tuff. It is a soft volcanic rock that is easy to carve but hardens when exposed to air. This stuff has been used as a building material in many places and ages. Easter Island statues are apparently carved of it.
Of course this activity is labor intensive you needs slaves, desperate people, or well paid laborers to dig the stone.
ETA: Tuff is a kind of limestone so it is going to dissolve in water. Some tunnels could be naturally carved by water but you don't want a whole underground complex undermined by dissolving stone. Romans were known to use lead to line pipes. It is soft and easy to pound into thin watertight sheets. You just don't want to be involved in its manufacture or live down stream.