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G. Lacedelli et al., We present a precise characterization of the TOI-561 planetary system obtained by combining previously published data with TESS and CHEOPS photometry, and a new set of 62 HARPS-N radial velocities (RVs). Our joint analysis confirms the presence of four transiting planets, namely TOI-561 b (P = 0.45 d, R = 1.42 R⊕, M = 2.0 M⊕), c (P = 10.78 d, R = 2.91 R⊕, M = 5.4 M⊕), d (P = 25.7 d, R = 2.82 R⊕, M = 13.2 M⊕), and e (P = 77 d, R = 2.55 R⊕, M = 12.6 R⊕). Moreover, we identify an additional, long-period signal (>450 d) in the RVs, which could be due to either an external planetary companion or to stellar magnetic activity. The precise masses and radii obtained for the four planets allowed us to conduct interior structure and atmospheric escape modelling. TOI-561 b is confirmed to be the lowest density (ρb = 3.8 ± 0.5 g cm−3) ultra-short period (USP) planet known to date, and the low metallicity of the host star makes it consistent with the general bulk density-stellar metallicity trend. According to our interior structure modelling, planet b has basically no gas envelope, and it could host a certain amount of water. In contrast, TOI-561 c, d, and e likely retained an H/He envelope, in addition to a possibly large water layer. The inferred planetary compositions suggest different atmospheric evolutionary paths, with planets b and c having experienced significant gas loss, and planets d and e showing an atmospheric content consistent with the original one. The uniqueness of the USP planet, the presence of the long-period planet TOI-561 e, and the complex architecture make this system an appealing target for follow-up studies., CHEOPS is an ESA mission in partnership with Switzerland with important contributions to the payload and the ground segment from Austria, Belgium, France, Germany, Hungary, Italy, Portugal, Spain, Sweden, and the United Kingdom. The CHEOPS Consortium gratefully acknowledge the support received by all the agencies, offices, universities, and industries involved. Their flexibility and willingness to explore new approaches were essential to the success of the mission. This work is based on observations made with the Italian Telescopio Nazionale Galileo (TNG) operated on the island of La Palma by the Fundación Galileo Galilei of the INAF at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias (GTO program, and A40TAC_23 program from INAF-TAC). The HARPS-N project was funded by the Prodex Program of the Swiss Space Office (SSO), the Harvard University Origin of Life Initiative (HUOLI), the Scottish Universities Physics Alliance (SUPA), the University of Geneva, the Smithsonian Astrophysical Observatory (SAO), and the Italian National Astrophysical Institute (INAF), University of St. Andrews, Queen’s University Belfast and University of Edinburgh. This paper includes data collected by the TESS mission, which are publicly available from the Mikulski Archive for Space Telescopes (MAST). Funding for the TESS mission is provided by the NASA Explorer Program. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This research has made use of data obtained from the portal http://www.exoplanet.eu/ of The Extrasolar Planets Encyclopaedia. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. GL acknowledges support by CARIPARO Foundation, according to the agreement CARIPARO-Università degli Studi di Padova (Pratica n. 2018/0098). TW and ACC acknowledge support from STFC consolidated grant numbers ST/R000824/1 and ST/V000861/1, and UKSA grant number ST/R003203/1. YA, MJH, B-OD, and ML acknowledge the support of the Swiss National Fundation under grant numbers 200020_172746, PP00P2-190080, and PCEFP2_194576. SH gratefully acknowledges CNES funding through the grant number 837319. GPi, VNa, GSs, IPa, LBo, and RRa acknowledge the funding support from Italian Space Agency (ASI) regulated by ‘Accordo ASI-INAF n. 2013-016-R.0 del 9 luglio 2013 e integrazione del 9 luglio 2015 CHEOPS Fasi A/B/C’. ADe acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (project FOUR ACES, grant agreement No. 724427), and from the National Centre for Competence in Research ‘PlanetS’ supported by the Swiss National Science Foundation (SNSF). KR is grateful for support from the UK STFC via grant number ST/V000594/1. This work has been supported by the National Aeronautics and Space Administration under grant number NNX17AB59G, issued through the Exoplanets Research Program. S.S. has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 833925, project STAREX). MG is an F.R.S.-FNRS Senior Research Associate. VVG is an F.R.S-FNRS Research Associate. LD is an F.R.S.-FNRS Postdoctoral Researcher. This work has been carried out within the framework of the NCCR PlanetS supported by the Swiss National Science Foundation. AMu and MF acknowledge support from the Swedish National Space Agency (career grant numbers 120/19C, DNR 65/19, 174/18). ABr was supported by the SNSA. We acknowledge support from the Spanish Ministry of Science and Innovation and the European Regional Development Fund through grant numbers ESP2016-80435-C2-1-R, ESP2016-80435-C2-2-R, PGC2018-098153-B-C33, PGC2018-098153-B-C31, ESP2017-87676-C5-1-R,MDM-2017-0737 Unidad de Excelencia Maria de Maeztu-Centro de Astrobiología (INTA-CSIC), as well as the support of the Generalitat de Catalunya/CERCA programme. The MOC activities have been supported by the ESA contract no. 4000124370. SGS, SCCB, and VA acknowledge support from FCT through FCT contract nr. CEECIND/00826/2018, POPH/FSE (EC), nr. IF/01312/2014/CP1215/CT0004, and IF/00650/2015/CP1273/CT0001, respectively. ODSD is supported in the form of work contract (DL 57/2016/CP1364/CT0004) funded by national funds through FCT. XB, SC, DG, MF, and JL acknowledge their role as ESA-appointed CHEOPS science team members. The Belgian participation to CHEOPS has been supported by the Belgian Federal Science Policy Office (BELSPO) in the framework of the PRODEX Program, and by the University of Liège through an ARC grant for Concerted Research Actions financed by the Wallonia-Brussels Federation. This work was supported by FCT – Fundação para a Ciência e a Tecnologia through national funds and by FEDER through COMPETE2020 – Programa Operacional Competitividade e Internacionalizacão by these grants UID/FIS/04434/2019, UIDB/04434/2020, UIDP/04434/2020, PTDC/FIS-AST/32113/2017 & POCI-01-0145-FEDER-032113,PTDC/FIS-AST/28953/2017 & POCI-01-0145-FEDER-028953,PTDC/FIS-AST/28987/2017 & POCI-01-0145-FEDER-028987. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (project FOUR ACES, grant agreement no. 724427). DG and LMS gratefully acknowledge financial support from the CRT foundation under grant number 2018.2323 ‘Gaseousor rocky? Unveiling the nature of small worlds’. KGI is the ESA CHEOPS Project Scientist and is responsible for the ESA CHEOPS Guest Observers Programme. She does not participate in, or contribute to, the definition of the Guaranteed Time Programme of the CHEOPS mission through which observations described in this paper have been taken, nor to any aspect of target selection for the programme. This work was granted access to the HPC resources of MesoPSL financed by the Region Ile de France and the project Equip@Meso (reference ANR-10-EQPX-29-01) of the programme Investissements d’Avenir supervised by the Agence Nationale pour la Recherche. PM acknowledges support from STFC research grant number ST/M001040/1. This work was also partially supported by a grant from the Simons Foundation (PI: Queloz, grant number 327127). GyMSz acknowledges the support of the Hungarian National Research, Development and Innovation Office (NKFIH) grant K-125015, a PRODEX Institute Agreement between the ELTE Eötvös Loránd University and the European Space Agency (ESA-D/SCI-LE-2021-0025), the Lendület LP2018-7/2021 grant of the Hungarian Academy of Science and the support of the city of Szombathely. This work is partly supported by JSPS KAKENHI grant number JP18H05439, JST CREST grant number JPMJCR1761, the Astrobiology Center of National Institutes of Natural Sciences (NINS) (grant number AB031010). EE-B acknowledges financial support from the European Union and the State Agency of Investigation of the Spanish Ministry of Science and Innovation (MICINN) under the grant number PRE2020-093107 of the Pre-Doc Program for the Training of Doctors (FPI-SO) through FSE funds.