What I had envisioned was power source connected to the first transformer's primary and that transformer's secondary connected to the next transformer's primary and so on. If this won't work to achieve higher and higher voltages, why not and is there a workaround?
In other words this?
I have highlighted why this will not work in red text. The first transformer will have 900VAC between the primary and secondary, the next one will have 9000VAC etc. In short order the voltage difference between the primary and secondary will be large enough to cause arcing from the secondary, back to the primary and from the primary back to the secondary as shown by the dotted red line.
Notice I placed small caps between primary and secondary (internal stray capacitance from secondary to primary), the limit is the breakdown voltage of this capacitance. Which is probably no more than a 1000V or less.
Your second question about what to do about this. I really don't think there is anything you can do about this. Even if you could achieve 1MV. The next problem is the load on the output must draw very little to no current. Imagine in what I have shown that the current to output stages is 10 milliamps that would make the input current 10 Amps to maintain that.
What are you trying to accomplish by doing this? Would a high DC voltage be acceptable?
There are few circuits around that can handle 1MV or more. I would recommend building a Tesla Coil.