Date: 201902
Local time of day: 1201-1800
Location: PAE.Airport, WA
Flight conditions: IMC
Weather elements / visibility: Icing; Snow
Light: Daylight
Aircraft: Commercial Fixed Wing
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Ferry / Re-Positioning
Flight phase: Climb; Takeoff / Launch
Airspace: Class B SEA
ATC / advisory: TRACON S46; Tower PAE
Reporter organization: Air Carrier
Reporter function: Pilot Not Flying; First Officer
Reporter qualification: Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Human factors: Communication Breakdown; Distraction; Situational Awareness
Second reporter function: First Officer; Pilot Not Flying
Anomaly: Conflict NMAC; Deviation - Altitude Overshoot; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Detector: Automation Aircraft TA; Automation Aircraft RA; Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Air Traffic Control Separated Traffic; Flight Crew Requested ATC Assistance / Clarification; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Took Evasive Action
Contributing factors: Chart Or Publication; Airspace Structure; Environment - Non Weather Related; Procedure; Human Factors
Primary problem: Human Factors

Narrative: I was in and out of the aircraft three times coordinating [de-icing/anti-ice] (no ground headset communications). As I left the cockpit for the walk around; I heard the First Officer calling for a verbal clearance; but did not hear the clearance or read back. After walk around I closed the cabin door; armed; readied the cabin; and returned to the cockpit. First Officer explained that Clearance Delivery changed the flight plan; which was input into the FMC; and confirmed with the Captain by stepping through the legs. I was told 10;000 feet was the cleared altitude as set in the MCP. At the same time I was ensuring that our HOT (Holdover Time) application was activated; as we had been treated with Type 4. Began towing immediately.Taxi distractions. Civilian car stuck on side of taxiway; requiring tug to veer off centerline and coordination to take us onto Taxiway A for start. Landing distance assessment. Captain tasked me with calling load control (cell phone) to coordinate closeout. We were approaching the departure point when Tower cleared us for takeoff without altitude assignment. Captain requested more time before takeoff to go over recently acquired closeout. Takeoff clearance was cancelled. When ready; takeoff clearance was granted a second time; without an altitude assignment; with Tower requesting a PIREP on cloud base. Takeoff uneventful. Tower handed us off to Departure; and Tower asked for a base report. First Officer responded with a [bases] report. Switched to Departure. Before check-in; Departure was already calling for us to level off at 3000 feet and calling traffic; initially at 3 o'clock and then 9 o'clock. Captain's NAV range was at 5 miles; and traffic was not visible on TCAS. He changed the range so the traffic could be seen at 9-10 o'clock.Approaching 3000 feet MSL; in rapid succession; Captain hand-flying; TCAS TA traffic alert; ATC call to level at 3000 feet; ATC call of traffic; TCAS RA to descend. First Officer and I both called for a descent to 3000 feet. Captain was slow to respond as he and I were looking at the converging traffic. Traffic in sight 9 o'clock high; TCAS RA. We finally started descending at 3800 feet; showing 400 feet separation. Descended to 3000 feet. After RA we descended to 3000 feet and assigned 120 heading. Autopilot was engaged at some point after the RA. Captain did not Heading Select 120; but instead began a discussion about what happened. I insisted that we needed to turn another 30 degrees to the left to a heading of 120. ATC then told us to fly 110 degrees. I insisted he Heading Select to the heading. Captain reached up and began turning the Airspeed Selector to a lower airspeed; thinking he was turning the Heading Select. I began to give loud and directive inputs to get him to reset the airspeed and instead turn the heading selector. He finally complied. 5 minutes later I found paperwork that appeared to be our departure clearance; which had a handwritten annotation of 3000 feet.Captain and First Officer had set the wrong departure altitude in the MCP; and were actively flying to the wrong altitude. [I] was not in cockpit when clearance was obtained. Captain and First Officer briefed me that clearance had given us a climb altitude that was incorrect. When ACARS printed clearance is not available; all pilots should be present for clearance request and read back.


Second narrative: On PAINE 6 Departure; no altitude assigned by ATC Tower. We responded to TCAS RA. ATC advised stop climb; we complied with TCAS; ATC vectors and altitudes. During preflight; we set standard 10;000 feet by habit. Clearance Delivery gave new routing and 3;000 feet (Relief First Officer was not present; executing exterior duties). Due to multiple distractions; entering revised route in FMS; deicing procedures; HOT (Holdover Time) calculations; calls to [ground handling Company] representative; non-standard operations; snow drifts; vehicle stalled in the taxiway; low ceiling; and unfamiliar airport; the MCP altitude was not correctly reset. While approaching number 1 for Runway 16R; I intended to query altitude with Paine Tower per SID (Page 10-3) but was distracted with a late closeout. All checklists completed. Uneventful takeoff. Full motor; cold day; empty plane; high performance; which resulted in the following events to occur rapidly. Immediately after takeoff; Paine Tower requested base of clouds; which I complied after a delay to achieve a safe altitude and aircraft control above 400 feet (which briefly delayed switchover to SEA Departure 128.5). On climb out; at approximately 3000 MSL; I heard 'Stop Climb' over 128.5 and immediately ordered level off; along with the Relief First Officer calls/direction; which the Captain promptly did by hand-flying. This maneuver was aided by TCAS RA indications and visual contact of the traffic. Peak altitude was approximately 3800 MSL; with closest point 400 feet vertical separation below corporate traffic. Lateral separation unknown. Relief First Officer did a great job keeping eyes on safety.To aid fellow pilots; triple check altitudes; do your best to mitigate continuous distractions; highlight altitudes on the paper clearance (to separate from the routing jargon); and possibly add non-standard notes to the airport 10-7 page (SEA dense traffic; expect X altitude when departing south; query Tower; inbound A-7 taxiway; turn onto Taxiway E and shut down; tow to parking; [ground handling Company]/Maintenance frequencies; etc.).


Synopsis: Air carrier flight crew reported climbing above the assigned departure altitude into a confliction with crossing traffic.