A positive-working multi-layer lithographic printing plate precursor has an inner imageable layer disposed over a substrate. This inner imageable layer comprises one or more first polymeric binders that are present in a total amount of at least 50 weight % and up to and including 97 weight %, based on total inner imageable layer dry weight. The precursor also has an ink-receptive outer imageable layer disposed over the inner imageable layer and this ink-receptive outer imageable layer comprises one or more second polymeric binders that are different than the first polymeric binder. Each of the one or more first polymeric binders has a weight average molecular weight of at least 200,000 and can also have a polydispersity of at least 4.