Force spectroscopy on the single-molecule level allows the investigation of intramolecular as well as interdomain and intermolecular interactions of both synthetic and natural polymers. In these experiments, a single molecule is usually stretched between two strong attachment points. The force then increases with increasing extension. Under certain conditions, however, force-extension curves result in force plateaus; an increase in extension is observed under constant force. These plateaus do not depend on pulling speed and therefore indicate transitions at equilibrium. Here we present single-molecule data where carboxymethycellulose (CMC) molecules are pulled out of a polymer film into a poor solvent. The resulting force-extension curves show not only one but up to seven force plateaus. The step height from one force plateau to the next is nonuniform but follows a characteristic spacing. This is the first time that nonuniform force plateaus are reported for polymer molecules. A simple model for the polymer-polymer and polymer-solvent interactions explains the measured data. In this model the new solvent-polymer interface gain during the pull is minimized by the formation of a tightly packed polymer bundle. By introducing a parameter for the product of effective radius of the polymer multiplied by surface tension, as well as a second parameter describing the interaction between polymer strands in the bundle, one finds excellent agreement between predicted and measured plateau heights. This model, therefore, provides a basis to investigate the interactions of polymer chains and the influence of solvent in well-defined geometries using single-molecule force spectroscopy.