oscilloscope, spectrum analyser etc

There is little that can be done with the receiver itself. Modern electronics are getting smaller and more integrated. You will also have a hard time finding data sheets since they are behind NDA agreements.

There are some single digit improvements for things like gain settings, cooling, EMI reduction. This might be very interesting to some but is not where I would start since the improvements are so small.

The main improvement are gained from the antenna and the feed line. There are a lot of posts on the ADSB forum because people are seeing huge improvements (double digits) for something they can do without fancy electronic equipment. With some equipment you might be able to optimize a bit more.