Topological swirling spin textures, such as skyrmions and merons, have recently attracted much attention as potential building blocks for high-density magnetic information devices. Controlling the transformation between different types of these quasiparticles is an important challenge. To date, these transitions have mostly been limited to a few non-centrosymmetric systems, where they are driven by the Dzyaloshinskii–Moriya interaction. Here we demonstrate multistep topological transitions among a variety of meron and skyrmion crystal states in a centrosymmetric magnet GdRu2Ge2. These are governed by the competition between Ruderman–Kittel–Kasuya–Yosida interactions at inequivalent wave vectors. These findings demonstrate that even a simple centrosymmetric magnet with competing interactions can be a promising material platform to realize a richer variety of magnetic quasiparticles with distinctive symmetry and topology, whose stability can be tuned by various external stimuli.