Narrative:

We were assigned 6000 ft and 080 heading; followed by a call from luke approach about traffic at our 11 o'clock 1000 ft below us. I was the non-flying pilot and was in the right seat; therefore I could not make visual contact with the cessna at 11 o'clock below the airplane. A TCAS target was displayed at this location relative to our airplane and showed a hollow blue diamond climbing at 1000 ft below us. While searching for the cessna visually; I noticed two aircraft at out 1 o'clock; approximately 4 miles away; level with us. I immediately queried luke approach as to the 1 o'clock traffic which was crossing from our right-to-left (coming from the direction of luke AFB) the controller stated there was a flight of F-16s at our 1 o'clock position; so I asked him if they intended to climb. At this point the pilot flying (PF) made visual contact with the cessna at 11 o'clock; noticed it was climbing and heading towards us; and began a gradual climb to avoid. Then the TCAS RA announced 'monitor vertical speed' (with red from 0 to 1500 FPM climb) I immediately told the pilot flying to descend; but he was continuing to avoid the cessna below us; so I said much louder: 'descend now' and 'we have traffic above us; descend'. By this time our aircraft had climbed about 700 ft to avoid the cessna and the F-16s were climbing also; but at a greater rate than we were. The PF began a descent to avoid the F-16s and we missed the first 2 by about 1/2 mile laterally and 300 ft vertically. Two more F-16s crossed directly overhead about 1000 ft above us. Luke approach notified us of traffic (cessna) that was less of a threat than the F-16s; but did not notify us of the F-16s until I queried them. The simultaneous nature of multiple aircraft converging on the same point caused a little confusion and a lot of communications problems. In the end we used 'see and avoid' to safely place the airplane between all the other traffic.

Related reports:

Google
 

Original NASA ASRS Text

Title: A LJ60 encountered multiple traffic conflicts which required combining TCAS advisories with see and avoid maneuvering to ensure separation.

Narrative: We were assigned 6000 FT and 080 heading; followed by a call from Luke Approach about traffic at our 11 o'clock 1000 FT below us. I was the non-flying pilot and was in the right seat; therefore I could not make visual contact with the Cessna at 11 o'clock below the airplane. A TCAS target was displayed at this location relative to our airplane and showed a hollow blue diamond climbing at 1000 FT below us. While searching for the Cessna visually; I noticed two aircraft at out 1 o'clock; approximately 4 miles away; level with us. I immediately queried Luke Approach as to the 1 o'clock traffic which was crossing from our right-to-left (coming from the direction of Luke AFB) the controller stated there was a flight of F-16s at our 1 o'clock position; so I asked him if they intended to climb. At this point the Pilot Flying (PF) made visual contact with the Cessna at 11 o'clock; noticed it was climbing AND heading towards us; and began a gradual climb to avoid. Then the TCAS RA announced 'Monitor Vertical Speed' (with red from 0 to 1500 FPM climb) I immediately told the pilot flying to descend; but he was continuing to avoid the Cessna below us; so I said much louder: 'Descend now' and 'we have traffic above us; descend'. By this time our aircraft had climbed about 700 FT to avoid the Cessna and the F-16s were climbing also; but at a greater rate than we were. The PF began a descent to avoid the F-16s and we missed the first 2 by about 1/2 mile laterally and 300 FT vertically. Two more F-16s crossed directly overhead about 1000 FT above us. Luke Approach notified us of traffic (Cessna) that was less of a threat than the F-16s; but did not notify us of the F-16s until I queried them. The simultaneous nature of multiple aircraft converging on the same point caused a little confusion and a lot of communications problems. In the end we used 'see and avoid' to safely place the airplane between all the other traffic.

Data retrieved from NASA's ASRS site as of April 2012 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.