We present the characterisation of the TOI-6041 system, a bright (V = 9.84 ± 0.03) G7-type star hosting at least two planets. The inner planet, TOI-6041 b, is a warm Neptune with a radius of 4.55−0.17+0.18 R⊕, initially identified as a single-transit event in TESS photometry. Subsequent observations with TESS and CHEOPS revealed additional transits, enabling the determination of its 26.04945−0.00034+0.00033 orbital period and the detection of significant transit-timing variations (TTVs), exhibiting a peak-to-peak amplitude of about 1 hour. Radial-velocity (RV) measurements obtained with the APF spectrographs allowed us to place a 3σ upper mass limit of 28.9 M⊕ on TOI-6041 b. In addition, the RV data reveal a second companion, TOI-6041 c, on an 88 d orbit, with a minimum mass of 0.25 MJup. A preliminary TTV analysis suggested that the observed variations could be caused by gravitational perturbations from planet c; however, reproducing the observed amplitudes requires a relatively high eccentricity of about 0.3 for that planet. Our dynamical stability analysis indicates that such a configuration is dynamically viable and places a 1σ upper limit on the mass of TOI-6041 c at 0.8 MJup. An alternative is the presence of a third, low-mass planet located between planets b and c, or on an inner orbit relative to planet b ─ particularly near a mean-motion resonance with planet b ─ which could account for the observed variations. These findings remain tentative, and further RV and photometric observations are essential in to better constrain the mass of planet b and to refine the TTV modeling, thereby improving our understanding of the system’s dynamical architecture.
