Air carrier First Officer reported being cleared for the BUR Runway 8 approach but having to go around after receiving TCAS RA alerts for VFR traffic at underlying airport VNY.

Narrative

On the ILS Z for Runway 8; when cleared for the approach we're told use caution for aircraft in Van Nuys traffic pattern. Weather was 6 SM OVC 014. Aircraft in front of us on the approach executed a go-around due to RA from VFR traffic in Van Nuys. Inside BUDDE; on the glide path we started seeing contacts below us on TCAS. At approximately 2;300 ft. MSL and still IMC; we got an RA; two aircraft 500 ft. - 600 ft. below; with an audible monitor vertical speed" and immediate "level off; level off." I responded to the RA and executed a go-around; TCAS "clear of conflict" very shortly after go-around started. Set up for another attempt at ILS Z Runway 8 with same discussion about VFR traffic. At the same point of the approach; inside BUDDE on the glide path; we got another RA off VFR traffic below us. I leveled off following TCAS RA and immediately got "clear of conflict." We were just below the clouds and able to recapture the glide path and runway environment to continue the approach and land uneventfully. I think the FAA should investigate the Van Nuys VFR pattern procedures. Is there a need to fly the pattern east of the field; below IFR traffic on approaches to BUR? Could the pattern be shifted/only flown to the west of the field to increase deconfliction with BUR traffic? Are the pilots actually following VFR cloud clearances? BUR is a short runway with terrain around the field; creating a demanding landing environment. Allowing Van Nuys VFR traffic to impact instrument approaches into BUR could result in an unstable approach and possible long/fast landing."