Dilute solutions of strongly charged polymer electrolytes undergo, upon addition of multivaltent salt to the solutions, a phase transition from extended to collapsed or bundled conformations. Upon further addition of salt they experience a second transition, a redissolution back into extended conformations. This paper presents a theoretical study of the structure and properties of the phase diagram of these solutions. On the basis of phenomenological observations a schematic phase diagram is constructed that allows a simple and explicit determination of the direction of the tie lines within the coexistence region. The actual shape of the coexistence boundary is determined by means of a model mean free energy functional that explicitly includes the possibility of association of both counterions and co-ions to the electrolytes. It is found that it is possible to redissolve the electrolytes into conformations where the bare charge of the electrolytes is overcompensated by the counterions but, due to the associated co-ions, can have either sign of total effective charge. When co-ion association is possible, the redissolution approximately coincides with the reassociation of the co-ions and counterions in the bulk of the solution.