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We present the study of seven systems, three of which TOI-2295, TOI-2537, and TOI-5110 are newly discovered planetary systems. Through the analysis of TESS photometry, SOPHIE radial velocities, and high-spatial resolution imaging, we found that TOI-2295b, TOI-2537b, and TOI-5110b are transiting warm Jupiters with orbital periods ranging from 30 to 94 d, masses between 0.9 and 2.9 MJ, and radii ranging from 1.0 to 1.5 RJ. Both TOI-2295 and TOI-2537 each harbor at least one additional, outer planet. Their outer planets TOI-2295c and TOI-2537c are characterized by orbital periods of 966.5 +/- 4.3 and 1920^{+230}_{-140} d, respectively, and minimum masses of 5.61^{+0.23}_{-0.24} and 7.2 +/- 0.5 MJ, respectively. We also investigated and characterized the two recently reported warm Jupiters TOI-1836b and TOI-5076b, which we independently detected in SOPHIE RVs. Additionally, we study the planetary candidates TOI-4081.01 and TOI-4168.01. For TOI-4081.01, despite our detection in radial velocities, we cannot rule out perturbation by a blended eclipsing binary and thus exercise caution regarding its planetary nature. On the other hand, we identify TOI-4168.01 as a firm false positive. Finally, we highlight interesting characteristics of these new planetary systems. The transits of TOI-2295b are highly grazing, with an impact parameter of 1.056$^{+0.063}_{-0.043}$. TOI-2537b, in turn, is a temperate Jupiter with an effective temperature of 307+/-15 K and can serve as a valuable low-irradiation control for models of hot Jupiter inflation anomalies. We also detected significant transit timing variations (TTVs) for TOI-2537b, which are likely caused by gravitational interactions with the outer planet TOI-2537c. Finally, TOI-5110b stands out due to its orbital eccentricity of 0.75+/- 0.03, one of the highest planetary eccentricities discovered thus far., Comment: 46 pages, 21 figures, accepted for publication in A&A