Date: 201911
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: VMC
Aircraft: Cessna 402/402C/B379 Businessliner/Utiliner
Operator: Air Taxi
Operating under: Part 135
Mission: Passenger
Flight phase: Initial Approach
Airspace: Class B ZZZ
ATC / advisory: TRACON ZZZ
Second aircraft: B737 Next Generation Undifferentiated
Reporter organization: Air Taxi
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Human factors: Communication Breakdown; Situational Awareness
Anomaly: ATC Issue All Types; Conflict NMAC; Deviation - Altitude Excursion From Assigned Altitude
Detector: Automation Aircraft TA; Person Flight Crew
When detected: In-flight
Result: Flight Crew Took Evasive Action
Contributing factors: Procedure; Airspace Structure; Human Factors
Primary problem: Human Factors

Narrative: FO (First Officer) and myself operated from IRK to ZZZ. We departed IRK VFR received flight following and proceeded toward ZZZ at 5500 ft. As we approached ZZZ from the northwest we were handed off to ZZZ Approach and were told to expect Runway XX and to turn 15 degrees left. From the northwest this turn brings us on the left side of the airport and puts us right downwind Runway XX. After being handed off to ZZZ Approach and a number of heading and altitude assignments we were assigned a heading 210 and 3;500 feet. I do not believe these assignments were assigned at the same time but at the time of the event this what were assigned. We were then given a traffic advisory at our 11 o'clock Aircraft Y. We reported the traffic in sight and continued as assigned.As we both neared the approach course of XYR we noticed the aircraft turning inbound toward the airport and consequently directly toward us. I am unaware of what the other aircraft's altitude assignment was but from what I could see visually they were either at our altitude or slightly above. Uncomfortable with the situation; I asked Approach for an altitude change. I did not receive a reply. The Controller was busy and with the amount of time I had to make a safe decision we couldn't get a word in. As Aircraft Y approached; I made the decision to descend in order to avoid a collision. I was at 3;100 or 3;200 feet as Aircraft Y passed over my aircraft. While this was all taking place; I received an audible traffic alert from the GPWS and noticed the indication +3; which indicates only 300 feet above. After the aircraft passed and returning to the assigned altitude I was given a turn toward the airport and landed with no further incident. I believe this to be a near mid-air collision and I am reporting it as that. As the altitude of the other aircraft is unknown to me the visual distance between us certainly was a loss of separation.As we approach the airport from the east we have to cross the approach course of a runway that is actively being used for landing. This means that there is a potential for aircraft to cross paths as it did in this case. The 2 vectors that our aircraft received pointed us directly at each other during our 'base leg' mine was 210 and theirs 030 or thereabout. Finally; the Controller was clearly busy as we ineffectually tried to communicate with him and did not receive a response.




Synopsis: C402C Captain reported experiencing a near mid-air collision with another aircraft also on approach.