<BR /> Aims: The Gemini-Monoceros X-ray enhancement is a rich field for studying diffuse X-ray emission and supernova remnants (SNRs). Most SNRs in this part of the sky are notoriously difficult to observe due to their large extent. With the launch of the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) on board the Spektrum-Röntgen-Gamma platform in 2019, we are now able to fully study those objects for the first time with CCD resolution. Many of the SNRs in the vicinity are suspected to be very old remnants, which are severely understudied in X-rays due to numerous observational challenges. In addition, the identification of new faint large SNRs might help to solve the long-standing discrepancy between the observed and expected number of Galactic SNRs. <BR /> Methods: We performed a detailed X-ray spectral analysis of the entire Gemini-Monoceros X-ray enhancement and a detailed background analysis of the vicinity, which allowed us to model the background with a high precision inside the X-ray enhancement. We also made use of multiwavelength data to better understand the morphology and to constrain the distances to the different sources. Based on the spectral analysis, we estimated the properties of the sources and calculated a grid of model SNRs to determine the individual SNR properties. <BR /> Results: Most of the diffuse plasma of the Monogem Ring SNR is well described by a single nonequilibrium ionization (NEI) component with an average temperature of kT = 0.14 ± 0.03 keV. We obtain an age of ≈1.2 × 10<SUP>5</SUP> yr - consistent with PSR B0656+14 - for the Monogem Ring and an explosion energy typical for a core-collapse (CC) supernova (SN). In the southeast, we found evidence for a significant temperature enhancement and a second plasma component. Our findings show that a scenario of two SNRs at ≈300 pc is likely, with the new candidate having an age of ≈50 000 yr. We were also able to improve on previous results for the Monoceros Loop and PKS 0646+06 SNRs by disentangling the foreground diffuse emission of the Monogem Ring SNR. We obtained significantly higher temperatures than previous studies, and for PKS 0646+06 a much lower estimated age of the SNR. We also found a new SNR candidate G190.4+12.5 which most likely is located at D > 1.5 kpc, expanding into a low density medium at a high distance from the Galactic plane, with an estimated age of 40 000-60 000 yr.