Date: 202006
Local time of day: 1201-1800
Location: ZZZ.Tower, US
Flight conditions: VMC
Weather elements / visibility: 5
Light: Daylight
Aircraft: B767-300 and 300 ER
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Cargo / Freight / Delivery
Flight phase: Initial Approach
Airspace: Class D ZZZ
ATC / advisory: TRACON ZZZ
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Human factors: Time Pressure; Situational Awareness; Communication Breakdown
Second reporter function: Pilot Not Flying; First Officer
Anomaly: ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Unstabilized Approach
Detector: Automation Air Traffic Control; Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Flight Crew Executed Go Around / Missed Approach; Flight Crew Requested ATC Assistance / Clarification
Contributing factors: Human Factors; Procedure; Staffing
Primary problem: Staffing

Narrative: Approach was VERY busy. Controller gave us vectors; kept our speed high and altitude at ; feet. He repeatedly told other aircraft to stand by and request nothing that he was TOO BUSY. He then turned us to ZZZZZ at 4;600 feet and said we were cleared for the approach. We noted on the LDS that the wind was 250/13. We were very high for this but attempted to rejoin. Approx 3 miles from runway we noted we would not meet stabilized approach criteria and requested a go around. The controller immediately stated that was fine and to just make right traffic; maintain 2;300 feet and we were cleared to land [Runway] XX. We stated several times that we did not wish to do this and wanted a second ILS. This is a mountainous area and a right hand pattern coupled with a 13 kt tailwind; would be a bit busy. The controller gave us a heading and said maintain 2;300 feet. We started the turn and then he came back three more times; asking us if we were headed to ZZZ. Then he came back again and said to fly the published. We were in the turn he had first given us and he changed this two more times. We requested 6;000 feet since 2;300 feet is not acceptable for the published and he said to climb to 6;000 feet. Then he yelled that he had a terrain alert and we better turn faster. We had no terrain indications and we were well into the turn to ZZZ and were climbing to 6;000 feet. He then changed the altitude two more times and settled on 4;500 feet. He then changed his mind again and gave us several different headings to fly. He asked us several times what approach we wanted and again; he told several other pilots to ask for nothing as he was TOO BUSY. We were given headings back to ZZZZZ and descended to cross ZZZZZ at the appropriate altitude of 3;300 feet. He overshot the localizer with the headings by 50 degrees but we were able to re-establish on the LOC and maintained a stabilized approach to landing. The wind was steady down the entire glide path at 250/13-15 kts. I am writing this report not because I felt that anything was violated or not followed but rather because the communication was so poor that I am unclear as to what he was expecting us to do. He gave us so many different sets of directions that I want to be sure that we identify what transpired. The outcome was successful and at no point was the safety of the flight in question. We advised him that we could not fly the published as he requested because he gave us 2;300 feet! I think that threw him and it went downhill from there with respect to communication. He had so many other people he was working with that I think it was lost in the shuffle. We were able to complete the approach and we did not show any terrain conflict. I believe his indication was not recognizing the turn we were making? Not sure. Anyway; this really accentuates the need to be cognizant of the tailwind limitation and know that any additional altitude will most likely result in a go around. We were prepared for this; but not prepared for the controller to state cleared to land; right traffic; visual XX. It was hard to get a word in to state that this was not our intent or desire and that simply flying the published missed approach would have been much safer. The frequency was too busy to get a word in and I think this heightened his workload and confusion as well.


Second narrative: On daylight approach; the Approach Controller was very busy and task saturated; telling several VFR aircraft to call back in 5 minutes. We were given vectors and airspeeds; and were eventually cleared for ILS RWY XX opposite direction to traffic. Winds were 250/13 at altitude (approaching landing limits); but were reported less on deck. Because we were kept high and fast; and communications were congested on Approach and Tower; we were above glide slope and fast. Captain (Pilot Flying) made the correct call to go around. I informed Tower and Tower Controller was initially confused. I repeated and he told us to enter a right visual downwind and that we were number 1 for RWY XX. I felt the altitude we were given was insufficient so I asked for 2;500 feet. I misunderstood the direction from the Captain that the visual approach was acceptable; before I understood that she wanted vectors to ILS which I requested. We were told to fly the published but by this point were too far down range to do this properly. We informed the controller of this while doing our best to comply (climb to 6;000 and proceed ZZZ). Terrain was rising and we were issued a terrain alert and told to turn right and climb. We were already in the process of doing so.  At no point was the safety of the flight in question.  We received altitudes and vectors for another ILS; which initially caused us to overshoot final. We established a stable approach on parameters and landed without incident.


Synopsis: B767 flight crew reported receiving a CFIT alert from the Approach Controller. Pilot crew also described difficulty communicating with the very busy controller.