TOI-282 is a bright (V = 9.38) F8 main-sequence star known to host three transiting long-period (Pb = 22.9 d, Pc = 56.0 d, and Pd = 84.3 d) small (Rp ≍ 2─4 R⊕) planets. The orbital period ratio of the two outermost planets, namely TOI-282 c and d, is close to the 3:2 commensurability, suggesting that the planets might be trapped in a mean motion resonance. We combined space-borne photometry from the TESS telescope with high-precision HARPS and ESPRESSO Doppler measurements to refine orbital parameters, measure the planetary masses, and investigate the architecture and evolution of the system. We performed a Markov chain Monte Carlo joint analysis of the transit light curves and radial velocity time series, and carried out a dynamical analysis to model transit timing variations and Doppler measurements along with N-body integration. In agreement with previous results, we found that TOI-282 b, c, and d have radii of Rb = 2.69 ± 0.23 R⊕, Rc = 4.13−0.14+0.16 R⊕, and Rd = 3.11 ± 0.15 R⊕, respectively. We measured planetary masses of Mb = 6.2 ± 1.6 M⊕, Mc = 9.2 ± 2.0 M⊕, and Md = 5.8−1.1+0.9 M⊕, which imply mean densities of ρb = 1.8−0.6+0.7 g cm−3, ρc = 0.7 ± 0.2 g cm−3, and ρd = 1.1−0.2+0.3 g cm−3, respectively. The three planets may be water worlds, making TOI-282 an interesting system for future atmospheric follow-up observations with JWST and ELT.