About ten years ago, you could look through a copy of Flying or AOPA pilot and see ads for traffic alerters that looked at the squawk code, altitude, and relative signal strength to determine its own altitude, and approximately how far away other traffic was.
Before TIS-B, this was about the best you could do without spending several AMU an active TCAS system. Even without direction or position information, these would tell you that something was nearby, and worked well enough to justify a $400-500 price tag to the thousands of pilots that bought them.
Replicating that functionality with a RPi and dump1090 would be fairly straightforward: use dump1090's Mode C decoding, lock onto the strongest signal as ownship, and then put the rest of the targets through a transfer function. If any of the targets are within X hundred feet of your altitude and greater than Y dB strength, put up an alert.