Water soluble polymeric dyes and polymeric tandem dyes are provided. The polymeric dyes include a water solvated light harvesting multichromophore having a conjugated segment of aryl or heteroaryl co-monomers including branched non-ionic water soluble groups (WSG) comprising two or more water soluble polymers. In some cases, the branched non-ionic water soluble groups (WSG) of the present disclosure are capable of imparting solubility in water in excess of 50 mg/mL to the multichromophore. The polymeric tandem dyes further include a signaling chromophore covalently linked to the multichromophore in energy-receiving proximity therewith. Also provided are aggregation-resistant labelled specific binding members that include the subject water soluble polymeric dyes. Methods of evaluating a sample for the presence of a target analyte and methods of labelling a target molecule in which the subject polymeric dyes find use are also provided. Systems and kits for practicing the subject methods are also provided.