Saturn's convective storms usually fall in two categories. One consists of mid-sized storms similar to 2,000 km wide, appearing as irregular bright cloud systems that evolve rapidly, on scales of a few days. The other includes the Great White Spots, planetary-scale giant storms ten times larger than the mid-sized ones, which disturb a full latitude band, enduring several months, and have been observed only seven times since 1876. Here we report a new intermediate type, observed in 2018 in the north polar region. Four large storms with east-west lengths similar to 4,000-8,000 km (the first one lasting longer than 200 days) formed sequentially in close latitudes, experiencing mutual encounters and leading to zonal disturbances affecting a full latitude band similar to 8,000 km wide, during at least eight months. Dynamical simulations indicate that each storm required energies around ten times larger than mid-sized storms but similar to 100 times smaller than those necessary for a Great White Spot. This event occurred at about the same latitude and season as the Great White Spot in 1960, in close correspondence with the cycle of approximately 60 years hypothesized for equatorial Great White Spots. A series of four storms appeared on Saturn's northern polar region in 2018, unusually close to each other in space and time. By their dimension and the energy needed to form them, they appear to be a hitherto unobserved kind of storm at Saturn, intermediate between the regional- and the global-sized ones.