Widebody; Low Wing; 2 Turbojet Eng
Flight Crew Last 90 Days 250; Flight Crew Total 20400; Flight Crew Type 1800
Workload; Situational Awareness; Distraction; Confusion; Communication Breakdown; Time Pressure
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance; Flight Crew Took Evasive Action; Flight Crew Became Reoriented
Company Policy; Weather; Procedure
On the arrival; SFO ATIS was calling for 3 miles visibility and the Bridge Visuals to 28L and 28R.  After passing LOZIT on the GOLDEN GATE arrival; NORCAL advised us expect ILS 28R.  We set up and briefed ILS 28R.  Shortly after that NORCAL said change to ILS 28L.  On base NORCAL said change to ILS 28R; and cleared for the ILS 28R.  When NORCAL handed us off to SFO Tower about 2 miles prior to the bridge and we checked in with SFO tower they said after the bridge change to Runway 28L. We had ground contact visually and had approximately 4 miles visibility; but could not see the airport.  We felt that we would pick up the runway shortly. The First Officer; Pilot Monitoring; re-setup the FMC and flight directors for 28L and I took the airplane off autopilot and started a slight side step to the left; while we were waiting for the instruments to respond to the ILS 28L. Last minute runway change takes pilot monitoring out of the loop at a critical time. When the instruments responded to the reset we found ourselves to the left of the localizer; I believe this was due to a crosswind aloft from the East. As I was correcting for the localizer and just before deciding to go around because of the approach becoming unstable; the First Officer in the back right seat called the runway in sight to the right of the aircraft. Because of the conditions I decided the safest decision would be to continue to land. I discussed that with the 3 first officers and they agreed. I feel that NORCAL as well as SFO Tower do not realize that so many runway changes on an approach in IMC conditions is more difficult for the crew and takes them out of the loop at a critical time. I also feel that ATC does not realize how long it takes and how many steps there are to execute a runway change and properly brief each approach. I also feel that we as airline crew have a tendency to overly cooperate with ATC. I do not believe that our aircraft was in danger at any point but in retrospect I feel I should have either not accepted the clearance from tower to change runways or should have gone around in lieu of the change.
I believe the succession of approach changes (4) we received from LOZIT to final contributed to this event. I believe as a crew our willingness to comply with SFO tower's final clearance was the pivotal event. We should have responded 'Unable' and continued the approach to 28R. Instead; we attempted to change ILS approaches while inside the OM without visually acquiring the runway.
A flight crew flying the ILS Runway 28R approach to the bridge then a change to Runway 28L; with four miles visibility and still outside of 6 DME; was unable to get visual on Runway 28L. They then begin to go missed when the runway comes into view.  Captain elects to continue the landing.