We report the Transiting Exoplanet Survey Satellite (TESS) discovery of a three-planet system around the bright Sun-like star HD 22946 (V ≈ 8.3 mag), also known as TIC 100990000, located 63 pc from Earth. The system was observed by TESS in Sectors 3, 4, 30, and 31 and two planet candidates, labeled TESS Objects of Interest (TOIs) 411.01 (planet c) and 411.02 (planet b), were identified on orbits of 9.57 and 4.04 days, respectively. In this work, we validate the two planets and recover an additional single transit-like signal in the light curve, which suggests the presence of a third transiting planet with a longer period of about 46 days. We assess the veracity of the TESS transit signals and use follow-up imaging and time-series photometry to rule out false-positive scenarios, including unresolved binary systems, nearby eclipsing binaries, and contamination of the light curves by background or foreground stars. Parallax measurements from Gaia Early Data Release 3 together with broad-band photometry and spectroscopic follow-up by the TESS FollowUp Observing Program (TFOP) allowed us to constrain the stellar parameters of TOI-411, including its radius of 1.157 ± 0.025 R⊙. Adopting this value, we determined the radii for the three exoplanet candidates and found that planet b is a super-Earth with a radius of 1.48 ± 0.06 R⊕, while planets c and d are sub-Neptunian planets with radii of 2.35 ± 0.08 R⊕ and 2.78 ± 0.13 R⊕ respectively. Using dynamical simulations, we assessed the stability of the system and evaluated the possibility of the presence of other undetected, non-transiting planets by investigating its dynamical packing. We find that the system is dynamically stable and potentially unpacked, with enough space to host at least one more planet between c and d. Finally, given that the star is bright and nearby, we discuss possibilities for detailed mass characterisation of its surrounding worlds and opportunities for the detection of their atmospheres with the James Webb Space Telescope.