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The coupled quintessence model with disformal couplings is treated here to mimic the $Λ$CDM background. Using this approach, the quintessence potential does not have to be specified. The model considers a generic fluid coupled to the quintessence, which is specified to be either dark matter or a relativistic fluid. The background consists of a cosmological constant and another uncoupled generic fluid, to cater for three studied scenarios. The cosmological dynamics is investigated for the coupled quintessence model, whose disformal couplings depend on the equation of state of both generic fluids. The scenario, whereby both generic fluids are dark matter, was further analyzed for an expansion history of the mimicking model. The analysis confirms that the mass scale of the quintessence influences the disformal characteristics of the dynamical system, which is portrayed by the evolution of an effective conformal coupling.