Biomolecules inhabit a crowded living cell that is packed with high concentrations of cosolutes and macromolecules that result in restricted, confined volumes for biomolecular dynamics. To understand the impact of crowding on the biomolecular structure, the combined effects of the cosolutes (such as urea) and confinement need to be accounted for. This study involves examining these effects on the collapse equilibria of three model 32-mer polymers, which are simplified models of hydrophobic, charge-neutral, and uncharged hydrophilic polymers, using molecular dynamics simulations. The introduction of confinement promotes the collapse of all three polymers. Interestingly, addition of urea weakens the collapse of the confined hydrophobic polymer, leading to non-additive effects, whereas for the hydrophilic polymers, urea enhances the confinement effects by enhancing polymer collapse (or decreasing the polymer unfolding), thereby exhibiting an additive effect. The unfavorable dehydration energy opposes collapse in the confined hydrophobic and charge-neutral polymers under the influence of urea. However, the collapse is driven mainly by the favorable change in polymer-solvent entropy. The confined hydrophilic polymer, which tends to unfold in bulk water, is seen to have reduced unfolding in the presence of urea due to the stabilizing of the collapsed state by urea via cohesive bridging interactions. Therefore, there is a complex balance of competing factors, such as polymer chemistry and polymer-water and polymer-cosolute interactions, beyond volume exclusion effects, which determine the collapse equilibria under confinement. The results have implications to understand the altering of the free energy landscape of proteins in the confined living cell environment.