  We report the discovery of a multi-planetary system transiting the M0 V dwarf
HD 260655 (GJ 239, TOI-4599). The system consists of at least two transiting
planets, namely HD 260655 b, with a period of 2.77 d, a radius of R$_b$ =
1.240$\pm$0.023 R$_\oplus$, a mass of M$_b$ = 2.14$\pm$0.34 M$_\oplus$, and a
bulk density of $\rho_b$ = 6.2$\pm$1.0 g cm$^{-3}$, and HD 260655 c, with a
period of 5.71 d, a radius of R$_c$ = 1.533$^{+0.051}_{-0.046}$ R$_\oplus$, a
mass of M$_c$ = 3.09$\pm$0.48 M$_\oplus$, and a bulk density of $\rho_c$ =
4.7$^{+0.9}_{-0.8}$ g cm$^{-3}$. The planets were detected in transit by the
TESS mission and confirmed independently with archival and new precise radial
velocities obtained with the HIRES and CARMENES instruments since 1998 and
2016, respectively. At a distance of 10 pc, HD 260655 becomes the fourth
closest known multi-transiting planet system after HD 219134, LTT 1445 A, and
AU Mic. Due to the apparent brightness of the host star (J = 6.7 mag), both
planets are among the most suitable rocky worlds known today for atmospheric
studies with the JWST, both in transmission and emission.
