This exploratory study investigates the impact of eliminating role-based influences on cross-modal points of subjective equality (PSE) in brightness and loudness perception. The traditional magnitude production paradigm creates asymmetry in stimulus roles, linked to a regression effect wherein adjustments gravitate toward the mean of the stimulus range. A two-alternative forced choice paradigm with an adaptive staircase procedure was employed to obscure intensity adjustments and neutralize stimulus roles, aiming to experimentally manipulate the internal references posited by the theory of global psychophysics (Luce et al., 2010). This enables a focused investigation of the intensity-matching's cognitive representation within the theory. Cross-modal PSEs for fixed auditory and visual standards were assessed through paired comparison trials, with each standard repeatedly paired with various comparison intensities from the alternate modality. The resulting cross-modal PSEs were estimated at the individual level using a binomial mixture model (Kuss et al., 2005; Schütt et al., 2016). These estimates informed the global psychophysics model under the assumption of role-independent reference intensities (Heller, 2021). The results revealed a mixed pattern across the six subjects. We discuss the implications of the absence of a regression effect in cross-modal PSEs for the cognitive representations involved in intensity-matching judgments. This study contributes to the understanding of cognitive processes in cross-modal perception and the implications of eliminating stimulus role dependencies in psychophysical judgments.