  Multi-planet systems are important sources of information regarding the
evolution of planets. However, the long-period planets in these systems often
escape detection. HD 22946 is a bright star around which 3 transiting planets
were identified via TESS photometry, but the true orbital period of the
outermost planet d was unknown until now. We aim to use CHEOPS to uncover the
true orbital period of HD 22946d and to refine the orbital and planetary
properties of the system, especially the radii of the planets. We used the
available TESS photometry of HD 22946 and observed several transits of the
planets b, c, and d using CHEOPS. We identified 2 transits of planet d in the
TESS photometry, calculated the most probable period aliases based on these
data, and then scheduled CHEOPS observations. The photometric data were
supplemented with ESPRESSO radial velocity data. Finally, a combined model was
fitted to the entire dataset. We successfully determined the true orbital
period of the planet d to be 47.42489 $\pm$ 0.00011 d, and derived precise
radii of the planets in the system, namely 1.362 $\pm$ 0.040 R$_\oplus$, 2.328
$\pm$ 0.039 R$_\oplus$, and 2.607 $\pm$ 0.060 R$_\oplus$ for planets b, c, and
d, respectively. Due to the low number of radial velocities, we were only able
to determine 3$\sigma$ upper limits for these respective planet masses, which
are 13.71 M$_\oplus$, 9.72 M$_\oplus$, and 26.57 M$_\oplus$. We estimated that
another 48 ESPRESSO radial velocities are needed to measure the predicted
masses of all planets in HD 22946. Planet c appears to be a promising target
for future atmospheric characterisation. We can also conclude that planet d, as
a warm sub-Neptune, is very interesting because there are only a few similar
confirmed exoplanets to date. Such objects are worth investigating in the near
future, for example in terms of their composition and internal structure.
