Date: 202102
Local time of day: 0601-1200
Location: PAO.Airport, CA
Flight conditions: VMC
Weather elements / visibility: 10
Light: Daylight
Aircraft: Small Aircraft; Low Wing; 1 Eng; Fixed Gear
Operating under: Part 91
Flight plan: None
Mission: Training
Flight phase: Landing
Airspace: Class D PAO
ATC / advisory: Tower PAO
Second aircraft: Small Aircraft; High Wing; 1 Eng; Fixed Gear
Reporter function: Instructor
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Multiengine
Human factors: Communication Breakdown; Confusion
Anomaly: ATC Issue All Types; Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Took Evasive Action
Contributing factors: Airspace Structure; Procedure
Primary problem: Airspace Structure

Narrative: I am a CFI and I was flying a training mission with my client who is a licensed private pilot working on transition training to a new model aircraft (Aircraft X). This was my client's first flight in a Aircraft X. The lesson started with a detailed preflight; followed by a similarly detailed run-up. Once ready; we departed Palo Alto Airport for a familiarization flight in a practice area south and west of the airport. During our time in the practice area we maintained visual separation from another aircraft in the training area (each trying to stay in our own section of the training area; while we also maintained appropriate distances from scattered clouds in the area; and staying below the Bravo which starts at 4;000 in that area. During this time; we stayed in contact with the Tower having asked them for advisories during our training mission.After approximately 1 hour of Hobbs time (including the taxi and detailed run-up); we copied ATIS Quebec and informed the Tower that we would like to return to the field for the option; and closed traffic. We were instructed to fly over Stanford and enter the pattern for left traffic for Runway 31. We made our way as instructed and entered the left downwind for Runway 31. The Tower then told us that we were number 4 cleared to land; and that the traffic that we were following was roughly abeam us in the opposite downwind. We acknowledged the instruction and reported negative contact with the traffic to follow. Meanwhile; the Tower was very busy with numerous other traffic entering; leaving; and in the pattern. We were then told to extend our downwind; that we had extensive extensions into Moffett Field's airspace (it is very common for Palo Alto to have and use extensions into Moffett's airspace - this extension was even further than usual) and that the Tower would call our base. While extending; we saw our traffic to follow turn base and then final. But we continued downwind since the Tower said that they would call our base.Moments later; the Tower instructed us to fly 'straight towards the 31 numbers' which was a bit strange since we were so far from the runway (probably at least 3 miles at this point). But the frequency was very busy and it didn't seem to make sense (or even possible) to ask to verify the instruction. We turned left onto a long final and proceeded towards the runway. We were holding approximately 1;000 feet (+/- since my student was flying and this was their first time in the aircraft) this entire time on downwind; base and long final.Not too long after we turned long final; the Tower told us to climb 500 feet immediately for traffic. I immediately took the controls of the plane; quickly (re)checked nearby traffic on the G1000 MFD (with ADS-B traffic) and did a visual scan for traffic as I went full forward on the throttle; prop; and mixture and pitched the nose back for the climb. The quick scan of traffic (visual and ADS-B) did not indicate any traffic below or next to us; but it did indicate one aircraft above our altitude but not in the immediate vicinity. None-the-less; we tried to visually acquire the above traffic as we climbed.Moments later; the tower told us to stop our climb immediately and to turn right and fly directly towards Leslie Salt. Again; we immediately complied with the Tower's instructions as we continued to try to acquire and track any immediate threats visually. Just then; we saw another aircraft pass directly above us; slightly off to our left side; in very close proximity to our aircraft. The Tower then instructed us to make a right turn back to final for landing.I've been flying at PAO for nearly XX years; so I am familiar with how busy it can get. But even with that experience; it was particularly busy at this time. One of the things that I think was a factor in this situation was a partial callsign conflict. Our aircraft callsign ended in [--] while the callsign of another aircraft on frequency at the time ended in [--]. In fact; it is possible that the aircraft above us when we were instructed to climb; and the one that nearly collided with moments later; was the aircraft ending in [--]. My theory is that the instruction to climb was actually intended for Aircraft Y and not Aircraft X; and that the controller tried to stop our climb as soon as he noticed the error. Unfortunately; these problems were all compounded by the heavy radio traffic making it virtually impossible to verify instructions; especially in a timely fashion.My client and I replayed this whole incident both while still in the air; and during debrief on the ground; and we are both quite certain that we responded to our correct callsign and that this wasn't a case of us improperly (and unintentionally) responding to someone else's callsign. I wanted to use the G1000 PLAYback feature to check/verify the radio call; but; unfortunately; the radio traffic was so heavy that there was no way to use the replay feature successfully. I have replayed this entire situation a number of times trying to analyze what I could have / should have done differently to avoid getting this close to another aircraft. Unfortunately; I haven't really come up with a good answer given the details of the situation.Given that the only nearby traffic that I could observe at the time was the one above us; I could have held my attitude of 1;000 feet; in defiance of the Tower Controller's instruction; until I could verify that the climb instruction was for us; or until I could verify another nearby traffic threat. But this seems like a very bad idea. I have always operated that when ATC gives you an immediate traffic avoidance instruction that you follow that instruction immediately. There could have very well been another nearby aircraft that I was unaware of that was an even more of a threat that I was currently unaware of. Hence my immediate response as instructed.I believe that the similar sounding callsigns; heavy radio traffic; and large number of aircraft operating in the class Delta; all contributed to the confusion for all parties. I know that it made our task (mine and my client) much more difficult; and I believe that you could hear that in the voice and instructions of the Tower Controller and the other pilots. After landing; we opted to terminate rather than continue pattern operations. Once back in the flying club; we talked with another CFI and student who was flying (and returning to the airport) at the same time. I asked them if they heard the Tower 'trying kill us' and the CFIs response was 'yeah; the Tower Controller was clearly overwhelmed!' We asked him if he heard any indications that we responded to the wrong callsign. His response was 'no' and that; again; he thought that whole problem was that the Tower Controller was simply overwhelmed by the overall situation.I know that Palo Alto is an FAA Training Tower; and I'm fully understanding and supportive of that. But perhaps in this case maybe there should have been additional oversight of Tower operations; or at least a senior controller stepping in before the controller got too overwhelmed.




Synopsis: Flight Instructor reported frequency congestion; ATC overwhelmed; similar call signs; resulted in a NMAC.