We present the discovery and characterization of a new multi-planetary system around the Sun-like star K2-360 (EPIC 201595106). K2-360 was first identified in K2 photometry as the host of an ultra-short-period (USP) planet candidate with a period of 0.88 d. We obtained follow-up transit photometry, confirming the star as the host of the signal. High precision radial velocity measurements from HARPS and HARPS-N confirm the transiting USP planet and reveal the existence of an outer (non-transiting) planet with an orbital period of ∼10 d. We measure a mass of 7.67±0.75 M⊕ and a radius of 1.57±0.08 R⊕ for the transiting planet, yielding a high mean density of 11±2 g cm-3, making it the densest well-characterized USP super-Earth discovered to date. We measure a minimum mass of 15.2±1.8 M⊕ for the outer planet, and explore a migration formation pathway via the von Zeipel–Kozai–Lidov (ZKL) mechanism and tidal dissipation.