To study the possibility of overdoping with oxygen and, thus, an increase in the charge carrier density, n_H(100 K), in RE123 layers (RE = Eu, Gd) with the aim of increasing the critical current density, Jc, oxygenation was carried out in the pressure range of p_O2 = 1-160 bar and temperatures of T_S = 300-800 °C during τ = 3-12 h of commercial EuBCO and GdBCO coated conductors (CC), from which the protective Cu layer and, in half of the cases, the Ag layer were chemically removed before oxygenation. The evidences of overdoping were observed about what were witnessed an increase of n_H(100 K), reduction of c-lattice parameters of RE123 (RE = Eu, Gd) of superconducting layers, behavior of normalized resistivity before superconducting transition, and J_c variation, however, the conditions to achieve optimal doping were not found yet. Treatment under 100 bar of O₂ for 3 h of GdBCO_CC (with Ag layer) at 600 °C led to an increase in J_c (77 K, 0 T) from 2.57 to 2.67 MA/cm², n_H(100 K) increased from 6.55 × 10²¹ to 6.91 × 10²¹ cm^-3, and J_c(5 K, 0 T) = 28.94 MA/cm² was observed after the treatment. The increase in J_c (77 K, 0 T) from 2.10 to 2.28 MA/cm² for GdBCO_CC (without Ag layer) was observed after treatment at 300 °C under 100 bar of O₂ for 3 h. In the both cases c-parameter of Gd123 decreased from 1.1735(1) to 1.1731(0) nm. For EuBCO_СС after treatment a decrease in c-parameters of Eu123 was observed: from 1.1738(8) to 1.1734(5) nm (for the Ag-coated sample under 100 bar O₂ at 300 °C) and from 1.1740(2) to 1.1736(3) nm (for the sample without Ag under 160 bar O₂ at 800 °C), but we failed to increase n_H(100 K) and J_c of the studied samples. However, the studies are still ongoing.