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In this work we present the results of performing multi-parametric fitting of the paraboloid magnetosphere model (PMM) to magnetometer observational data obtained during a number of MESSENGER orbits around Mercury with the purpose of investigating the interplanetary magnetic field (IMF) coefficient of penetration into the magnetosphere. We analyze cases with multiple IMF states that satisfy the condition that during the inbound and outbound orbit segments the IMF vector is approximately the same; since Mercury’s magnetosphere is quite small, any disturbances in the magnetosphere induced by abrupt changes in the IMF propagate rapidly, and the magnetosphere achieves a new meta-stable state shortly. We thus assume that the IMF is nearly constant and the magnetosphere is quasi-stationary during the whole duration of these orbit segments, and fit the PMM parameters (including the IMF penetration coefficient κ) to match the observations.