Light Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 16.0
Situational Awareness; Workload
ATC Issue All Types; Conflict Airborne Conflict
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action; Flight Crew FLC complied w / Automation / Advisory
Procedure; Human Factors; Airspace Structure; Company Policy
I was working 4 positions combined; arrival east; arrival west; Boeing arrivals sector; and PAE sector. I had 4 frequencies with aircraft checking in and blocking each other.  Because I was working multiple sectors I was zoomed out much farther than normal to see all the airspace; so about a 80 mile range. Therefore it was difficult to see all the VFRs; and there were a lot of VFRs out. My scope was cluttered with VFR targets that no one was talking to. I was vectoring Aircraft X for a visual approach into RNT. I was also working multiple other aircraft and trying to look up an identifier for a destination. After I cleared Aircraft X; he was straight in to RWY 15. I saw a VFR aircraft at 2;000 feet to Aircraft X 10:00 3 miles converging. I called traffic; he didn't see him. He got closer. I called it again; he didn't see him. Now I couldn't turn left and cancel his clearance because that's where the VFR was. If I were to try to turn right; I would hit a higher MVA (minimum vectoring altitude) and have to climb into finals airspace where aircraft are descending into SEA; which would involve breaking out SEA arrivals and getting a point out which I didn't have time for. I can't remember if I called traffic two or three times; but the last time Aircraft X saw him and responded to an RA. Unfortunately I didn't see him earlier as data tags were overlapping; although I don't know if I could have avoided the aircraft anyway; as I am not talking to him and have no idea what he's doing. RNT airport; sea airport; and BFI airport are all within 3 miles of each other; surrounded by MVAs so there's not a lot of wiggle room. We have to push the RNT and BFI aircraft down really low below the bravo airspace to stay out of SEA finals way; and this forces aircraft to be tangled up with VFRs.  After this; the supervisor split sectors into a high/ low configuration which was better and allowed to see VFRs easier. The best solution to these IFR/VFR TCAS RA's which occur daily here is to somehow have protected airspace around BFI and RNT. Either Class C or lower the bravo to 2;000 feet. After this I split and worked only BFI and PAE sectors and I had another TCAS with an IFR/VFR  even though the IFR was delay vectored and altitude stopped 500 feet above. There's too much VFR traffic within that area that we aren't talking to and that makes things very dangerous; especially since a lot of them are at IFR altitudes.  The workload becomes intense because you are staring so hard at VFRs; trying to anticipate what they are going to do; and it takes your focus off of your other traffic.
A TRACON Controller reported a conflict with an aircraft they were vectoring for an approach and an unidentified VFR aircraft in airspace that routinely has situations such as this occur.