The presence of a permanent electric dipole moment in an elementary particle implies Charge-Parity symmetry violation and thus could help explain the matter-antimatter asymmetry observed in our universe. Within the context of the Standard Model, the electric dipole moment of elementary particles is extremely small. However, many Standard Model extensions such as supersymmetry predict large electric dipole moments. Recently, the muon electric dipole moment has become a topic of particular interest due to the tensions in the magnetic anomaly of the muon and the electron, and hints of lepton-flavor universality violation in B-meson decays. In this article, we discuss a dedicated effort at the Paul Scherrer Institute in Switzerland to search for the muon electric dipole moment using a 3-T compact solenoid storage ring and the frozen-spin technique. This technique could reach a sensitivity of 6 × 10−²³ 𝑒·cm after a year of data taking with the 𝑝 = 125 MeV/𝑐 muon beam at the Paul Scherrer Institute. This allows us to probe various Standard Model extensions not reachable by traditional searches using muon 𝑔 − 2 storage rings.