He skipped his team to a runner-up finish at the KMC Rocktoberfest and lost in the semifinals at the 2010 Horizon Laser Vision Center Classic as lead for Jamie Schneider.

The following season, he won the Moose Jaw Cash Spiel skipping his team of Matt Ryback, Dan Marsh and Aaron Shutra.

Following the season, Team Marsh disbanded, with Kevin and his brother Dan joining the Bruce Korte rink at third and second respectively.

[12] Their combined points earned them a spot in the 2017 Canadian Olympic Curling Pre-Trials where they finished 2–4, missing the playoffs.

[14] They wrapped up their season at the 2018 Humpty's Champions Cup, which they qualified for by winning the College Clean Restoration Curling Classic.

The team, led by Kirk Muyres, found success early by reaching the final of both the DeKalb Superspiel and the Medicine Hat Charity Classic.

[15] This earned them promotion into the Tier 1 slams which they competed in three of, the 2018 National, the 2019 Canadian Open and the 2019 Champions Cup, missing the playoffs at all of them.

[17] They then lost the 1 vs. 2 game 7–4 to favorites Matt Dunstone but were able to bounce back 7–6 in the semifinal over Ryan Deis to reach the final.

There, Team Muyres scored one in the tenth end to defeat Dunstone 6–5 and qualify for the 2019 Tim Hortons Brier, Marsh' first appearance at the Canadian men's championship.

In Grand Slam play, the team made the semifinals of the 2019 Tour Challenge Tier 2 event and missed the playoffs at the 2020 Canadian Open, going 0–3.

[22] Due to the COVID-19 pandemic in Canada, the qualification process for the 2021 Canadian Olympic Curling Trials had to be modified to qualify enough teams for the championship.

[25] Elsewhere on tour, the team had back-to-back semifinal finishes at the IG Wealth Management Western Showdown and the Nufloors Penticton Curling Classic.

After losing two games early in the triple knockout event, the team rallied off four straight victories to reach the provincial final where they faced the Dunstone rink.

[27] The win earned them the right to represent Saskatchewan at the 2022 Tim Hortons Brier where they finished with a 6–2 round robin record, including a victory over the Dunstone rink in the final draw.