  The Gemini-Monoceros X-ray enhancement is a rich field for studying diffuse
X-ray emission and supernova remnants (SNRs). With the launch of eROSITA
onboard the SRG platform in 2019, we are now able to fully study these sources.
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, identification of new faint large SNRs might help to solve the
long-standing discrepancy of observed and expected number of Galactic SNRs.
  We performed a detailed X-ray spectral analysis of the entire diffuse
structure and a detailed background analysis of the vicinity. We also made use
of multi-wavelength data to better understand the morphology and to constrain
the distances to the different sources. We estimated the plasma properties of
the sources and calculated a grid of model SNRs to determine the individual SNR
properties.
  Most of the diffuse plasma of the Monogem Ring SNR is well described by a
single non-equilibrium ionization (NEI) component with an average temperature
of $kT = 0.14\pm 0.03$ keV. We obtain an age of $\approx 1.2\cdot 10^5$ yr -
consistent with PSR B0656+14 - for the Monogem Ring. In the south-east, we
found evidence for a hotter second plasma component and a possible new SNR
candidate at $\approx 300$ pc, with the new candidate having an age of $\approx
50,000$ yr. We were also able to improve on previous studies on the more
distant Monoceros Loop and PKS 0646+06 SNRs. 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.
