The British number one, who took the first ever gold with brakeman Dan Money in the two-man event, made the podium to collect bronze in both the four-man races.
Jackson, who was aided by brakemen Dave FJ Smith, Bruce Tasker and Chris Woolley, said: "Going into these races we were pretty confident we could get a good result in St Moritz and I am really happy to have made the podium three times this week.
"It is a huge achievement for us and shows that we are on the right track for even more success this season."
British Bobsleigh performance director Gary Anderson said: "It was always our intention to target these races.
"This was highlighted at our pre-season planning meetings where the objective was to get a podium finish.
"It was thought for a number of factors that St Moritz would offer us the best opportunity to do just that.
"Coach Lee Johnston knows the environment and conditions at St Moritz which provided vital intelligence for us.
"Jackson and his crew, which included our newest recruit, Bruce Tasker, prepared well, got the sled set up right and produced outstanding performances.
"It is my intention to get the men's programme into a position where it attracts investment from the funding agencies.
"Performances like these illustrate that we can be competitive and, with three years to go until Sochi 2014, we can get the men's programme up to medal zone.
"I am delighted with these results and this must now become a regular occurrence."
In the women's two-bob Europa Cup races on Saturday, driver Fiona Harrison and brakewoman Victoria Olaoye achieved the fastest push of the race to take sixth place.
Kerry Morgan, with brakewoman Faye Pittman, took 10th and Gillian Cooke, with Kelly Denyer, finished 11th.
PR, marketing and sponsorship director of British Bobsleigh, Manny Cohen, said of the team's achievements this season: "The British invented the sport and as a non-ice nation it is great to see both the men's and women's teams producing great results in the Europa and World Cup.
"We still have a long way to go until Sochi 2014 but we will do everything in our power to ensure we can become a force to be reckoned with."
Corporal Jackson will next race in the World Cup in St Moritz later this week.
Meanwhile, Army corporal Paula Walker, who missed her World Cup race to be with her father, who is critically ill in hospital, will compete in the World Junior Championships with her crew of Kelly Denyer and Rebekah Wilson in Park City, Utah, from January 31.