Can we have multiple relationships with same name and different facet values between 2 nodes?

It is not possible to have 3 relations on the same edge. You would have to have multiple edges with different predicates. E.g. <HAS_STATUS_1>, <HAS_STATUS_2>, <HAS_STATUS_3>.

Another way is by doing an intermediate node queue. So, every relationship is a node instead of just Facets, you would have a complete Node. E.g. A1 => [R1, R2, R3, R4] => S1. You still could use facets between A1 and Rn* for convenience.