How plausible would it be to build an entire underground city beneath another city? Would it be structurally sound? And I do mean an entire city, underground with skyscrapers holding up the ceiling.
From the way the question is worded, I assume the upper city was built first, with the lower city retrofitted beneath.
The first priority in structural engineering is to transfer loads downward. The upper city is built on something, typically a layer of bedrock, so you have to preserve that support while you dig the space and install the load-bearing members. The deeper you go, the more weight you add to the total, because those members also support their own weight.
More plausible might be a dome over your lower city. A dome distributes weight to the edges while leaving the center open. Several small domes would be even better. On the other hand, you could have one tall parabolic opening.
Once you build this city, though, you run into infrastructure concerns. Where do you get food, water, fresh air, power, light? What do you do with garbage, sewage, smoke? How do you travel to and from the surface? What are the psychological effects of living in a hole?
A more plausible scenario might be to build the lower city upside down and share infrastructure with the upper city.
Completely plausible. As long as the roof of the underground city was structurally sound enough it should be possible. The farther underground the city, the less likely a collapse as then the earth itself can serve as a strong structural support. However as with any roof, they all have limits and after a certain amount of weight it will eventually cave. I would suggest making the roof of the underground city a dome as dome's are very architecturally sturdy. With strong materials, your underground city should be able to hold up the standard modern day city.
Soil on any world can be divided into its horizons, normally designated A,B,C,R. A= Surface Horizons the normal soil with a varying depth this is what we dig into to farm ect. Next is B= Subsoil tightly compressed but both A and B are to loose to hold the weight necessary for a city. So continuing to dig we hit C= Substratum this can be hundreds of meters thick, last you hit R= Bedrock. All of this strata will be varying depth. The most solid being the bedrock past that its just Magma. So build a "X" thick base on the topsoil, sink numerous columns down to bedrock to secure upper level. Next Find the thickness of the bedrock divide by 2 to find halfway point this is the base of your new city. Hollow out wider then it is tall, the height determined by the estimated weight supported by the upper layer of the bedrock, as you build the lower city be generous with the use of more columns from upper bedrock to lower bedrock.
technically it could be plausible, as long as the city on top mirrored the city underneath, otherwise the city on top would be too heavy. Eg. if there was a skyscraper on the top side, there would have to be a skyscraper underneath it as well. Then the floor/ceiling would have to be reinforced. Maybe