Water soluble light harvesting multichromophores having pendant chromophore groups are provided. The light harvesting multichromophore has a polymeric backbone including non-conjugated repeat units and a plurality of pendant donor chromophore groups linked to a non-conjugated repeat unit of the polymeric backbone. A pendant chromophore group can be a BODIPY group substituted with one or more water soluble groups. Polymeric tandem dyes based on the subject multichromophores are provided that further include an acceptor fluorophore linked to a non-conjugated repeat unit of the polymeric backbone and configured in energy-receiving proximity to a pendant donor chromophore group. Also provided are labelled specific binding members that include the subject polymeric tandem dyes. Methods of evaluating a sample for a target analyte and methods of labelling a target molecule in which the subject polymeric tandem dyes find use are provided. Systems and kits for practicing the subject methods are also provided.