The objective of this study is to analytically explore mass loss and gain induced by stellar collisions on a gas-accreting extremely massive star (aEMS, $ 10^3 ⊙ 10^4 $). We also consider its contribution to the mass budget in the context of forming multiple stellar populations (MPs) in a typical protoglobular cluster (GC). We used MESA to build a series of aEMS models up to $2 ⊙ $ for three Fe/H values, covering the metallicity range of Galactic GCs, with different treatments of super-adiabatic convection. We set analytical prescriptions to quantify collision-induced mass loss when a star spirals and deposits energy into the envelope of the aEMS. We used a Monte Carlo approach to simulate the effects of multiple collisions on an aEMS of initial mass of $10^3 M_ ⊙ $ in a static proto-GC, accounting for mass loss and gain from collisions, gas accretion, and stellar winds. We show that assumptions on super-adiabaticity in radiation-dominated layers significantly impact the aEMSs properties and their collision responses: extended stars tend to lose mass, while compact ones are more likely to gain it. Our MC simulations predict the total mass lost and gained, along with the corresponding timescales and contributions from stellar winds and collisions. The results are influenced by the structural characteristics of the aEMS and by the gas accretion rate during the collision phase. Under certain conditions, the EMS exhibits a "conveyor belt" behavior, processing up to $10^ M_ ⊙ $ of material in ∼ 5 Myrs. This study provides theoretical predictions supporting aEMSs as contributors to the abundance anomalies observed in GCs. It emphasizes the importance of including collision dynamics and mass transfer in aEMS formation and evolution models in dense stellar environments. We provide a grid of predictions for stellar M-R- Fe/H -structure relations and collision-induced mass loss and gain, suitable for inclusion in hydro and N-body simulations of star clusters.