Polymers in multicomponent solvents are key to understanding biomolecular condensates and promising systems for the preparation of polymer materials for achieving multi-stimuli-responsive properties. Examples of novel transition scenarios in multicomponent solvents are co-nonsolvency and the phase separation of water-soluble biomacromolecules, such as RNA, together with binding proteins. I discuss a simplified model describing polymers in the presence of solution components that adsorb onto the polymers and can form temporary bridges. Following previous work, these components are denoted as gluonic. While the spinodal behavior, i.e., the instability of multicomponent solutions, can be solved analytically within some approximations, the phase coexistence regions, i.e., the binodals, can only be calculated numerically. A partial equilibrium of the gluonic component can be obtained, and the resulting effective free energy can be analyzed using the convex hull algorithm, which allows one to explore regions in the phase diagram down to very low concentration levels that are typically realized for long polymers. As an example, I consider a biology-inspired system of mRNA and the protein PGL-3 in a lattice model, which leads to reasonable estimates of the phase behavior observed in in vitro experiments. Adding a component to the solution that preferentially binds to the polymer and blocks adsorption sites for the gluonic component can lead to dissolution of condensates. Due to the different binding affinities of the two components, a new type of LCST behavior can be observed in the limit of strong binding of the regulatory component, where equilibrium phase separation is induced by increasing the temperature.