Two Parameter Deformation of Embedding Class-I Compact Stars in Linear <i>f</i> ( <i>Q</i> ) Gravity

Recent multi-messenger observations, including gravitational wave detections of compact objects in the neutron star-black hole mass-gap region and precise measurements of high-mass pulsars, motivate mechanisms capable of enlarging the stellar mass window without arbitrarily stiffening the equation of state (EOS) toward the causal limit. In linear [Formula: see text] gravity of the form [Formula: see text], the theory is dynamically equivalent to General Relativity (GR) at the geometric level and modifies stellar structure solely through a uniform rescaling of the matter sector governed by [Formula: see text]. Consequently, linear [Formula: see text] alone does not introduce new geometric families of stellar solutions or alter classical compactness bounds. To overcome this structural limitation, we incorporate gravitational decoupling within an embedding class-I (Karmarkar) Vaidya-Tikekar configuration in linear [Formula: see text] gravity. While similar VT-based decoupling constructions exist in GR, the present framework introduces a controlled two-parameter deformation characterized by [Formula: see text]: the decoupling parameter [Formula: see text] governs geometric deformation and EOS stiffness, whereas [Formula: see text] independently rescales the matter sector without altering the metric structure. This separation permits a direct comparison between GR and linear [Formula: see text] gravity at fixed geometric deformation, thereby isolating pure coupling-driven mass enhancement. We determine the admissible parameter domain from regularity, matching, causality and compactness requirements and derive an analytic compactness bound for the decoupled embedding class-I configuration. We show that, at fixed [Formula: see text] (i.e., fixed effective stiffness), linear [Formula: see text] systematically shifts the mass-radius sequence relative to GR through matter-sector rescaling alone. The combined action of [Formula: see text] and [Formula: see text] enlarges the accessible stellar mass window while preserving physical acceptability, allowing configurations compatible with recent high-mass pulsars and mass-gap candidates without exceeding causal limits.