Context. The Kepler extended mission, also known as K2, has provided the community with a wealth of planetary candidates that orbit stars typically much brighter than the targets of the original mission. These planet candidates are suitable for further spectroscopic follow-up and precise mass determinations, leading ultimately to the construction of empirical mass-radius diagrams. Particularly interesting is to constrain the properties of planets that are between Earth and Neptune in size, the most abundant type of planet orbiting Sun-like stars with periods of less than a few years. Aims. Among many other K2 candidates, we discovered a multi-planetary system around EPIC 246471491, referred to henceforth as K2-285, which contains four planets, ranging in size from twice the size of Earth to nearly the size of Neptune. We aim here at confirming their planetary nature and characterizing the properties of this system. Methods. We measure the mass of the planets of the K2-285 system by means of precise radial-velocity measurements using the CARMENES spectrograph and the HARPS-N spectrograph. Results. With our data we are able to determine the mass of the two inner planets of the system with a precision better than 15%, and place upper limits on the masses of the two outer planets. Conclusions. We find that K2-285b has a mass of M_b = 9.68_−1.37^+1.21 M_⊕ and a radius of R_b = 2.59_−0.06^+0.06 R_⊕, yielding a mean density of ρ_b = 3.07_−0.45^+0.45 g cm⁻³, while K2-285c has a mass of M_c = 15.68_−2.13^+2.28 M_⊕, radius of R_c = 3.53_−0.08^+0.08 R_⊕, and a mean density of ρ_c = 1.95_−0.28^+0.32 g cm⁻³. For K2-285d (R_d = 2.48_−0.06^+0.06 R_⊕) and K2-285e (R_e = 1.95_−0.05^+0.05 R_⊕), the upper limits for the masses are 6.5 M_⊕ and 10.7 M_⊕, respectively. The system is thus composed of an (almost) Neptune-twin planet (in mass and radius), two sub-Neptunes with very different densities and presumably bulk composition, and a fourth planet in the outermost orbit that resides right in the middle of the super-Earth/sub-Neptune radius gap. Future comparative planetology studies of this system would provide useful insights into planetary formation, and also a good test of atmospheric escape and evolution theories.