Is there a rail pass for the Tokaido Shinkansen that residents can use?

My family is coming to visit for the winter holidays and they’re planning on buying the JR rail pass. The plan is to visit Osaka from Yokohama and we might possibly make more than one trip.

Multiple round-trip Shinkansen tickets is going to be super expensive but since I’m a resident, I can’t buy the JR rail pass.

Is there a pass that will let me ride the Tokaido Shinkansen for free within a certain number of days? Thanks