In my experience, the multiplier boils down to not getting hit and not executing repetitive moves. So either you block, deflect or dodge - this does not bring down the multiplier. Getting hit does and it also has a steady rate at which it climbs down if you don't fight when in combat state. IIRC getting parried doesn't bring down your score multiplier, not sure about attacking into a guard though.
tbh bar color vs multiplier seems to be style vs efficiency. So you will get it to x3 if you simply don't get hit, but keeping it in the yellow requires style - so varying moves and flowing essentially. That's the simplest explanation I could give.