The surface coverage of coarse-grained macromolecules bound to a solid substrate is not simply proportional to the two-dimensional number density because macromolecules can overlap. As a function of the overlap probability d, we have developed analytical formulas and computational models capable of characterizing this nonlinear relationship. For simplicity, we ignore site-site interactions that would be induced by length-scale mismatches between binding sites and the radius of gyration of the incident coarse-grained macromolecular species. The interactions between macromolecules are modeled with a finite bounded potential that allows multiple macromolecules to occupy the same binding site. The softness of the bounded potential is thereby reduced to the single parameter d. Through variation of this parameter, completely hard (delta = 0) and completely soft (delta = 1) behavior can be bridged. For soft macromolecular interactions (delta > 0), multiple occupancy reduces the fraction of sites ? occupied on the substrate. We derive the exact transition probability between sequential configurations and use this probability to predict phi and the distribution of occupied sites. Due to the complexity of the exact phi expressions and their analytical intractability at the thermodynamic limit, we apply a simplified mean-field (MF) expression for phi. The MF model is found to be in excellent agreement with the exact result. Both the exact and MF models are applied to an example dynamical system with multibody interactions governed by a stochastic bounded potential. Both models show agreement with results measured from simulation.