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We report the Transiting Exoplanet Survey Satellite (TESS) discovery of athree-planet system around the bright Sun-like star HD~22946(V=8.3 mag),alsoknown as TIC~100990000, located 63 parsecs away.The system was observed by TESSin Sectors 3, 4, 30 and 31 and two planet candidates, labelled TESS Objects ofInterest (TOIs) 411.01 (planet $c$) and 411.02 (planet $b$), were identified onorbits of 9.57 and 4.04 days, respectively. In this work, we validate the twoplanets and recover an additional single transit-like signal in the lightcurve, which suggests the presence of a third transiting planet with a longerperiod of about 46 days.We assess the veracity of the TESS transit signals anduse follow-up imaging and time series photometry to rule out false positivescenarios, including unresolved binary systems, nearby eclipsing binaries orbackground/foreground stars contaminating the light curves. Parallaxmeasurements from Gaia EDR3, together with broad-band photometry andspectroscopic follow-up by TFOP allowed us to constrain the stellar parametersof TOI-411, including its radius of$1.157\pm0.025R_\odot$. Adopting this value,we determined the radii for the three exoplanet candidates and found thatplanet $b$ is a super-Earth, with a radius of $1.72\pm0.10R_\oplus$, whileplanet $c$ and $d$ are sub-Neptunian planets, with radiiof$2.74\pm0.14R_\oplus$ and $3.23\pm0.19R_\oplus$ respectively. By usingdynamical simulations, we assessed the stability of the system and evaluatedthe possibility of the presence of other undetected, non-transiting planets byinvestigating its dynamical packing. We find that the system is dynamicallystable and potentially unpacked, with enough space to host at least one moreplanet between $c$ and $d$.(Abridged)

TESS discovery of a super-Earth and two sub-Neptunes orbiting the bright, nearby, Sun-like star HD 22946