If two items are added to a cell that are equivalent except for their weights or back-pointers, then they are merged (in the MT decoding literature, this is also known as hypothesis recombination), with the merged item taking its weight and back-pointers from the better of the two equivalent items.
(if we are interested in finding the k-best derivations, the merged item gets the multiset of all the tuples of back-pointers from the equivalent items.