yes you can cross razberry, blackberry, mullberry ,logan berry ,tay berry ,boisenberry ,dewberry together they all cross breed.
currents and goose berries do cross that is how you get
"jostaberries"
I have never heard of a cranberry blueberry cross cranberries grow on a vine while blue berries grow on a bush.

Mulberry(Morus spp., a tree) most likely will not hybridize with the canberries such as blackberry, raspberry, etc(Rubus spp., which are semi-woody perennials). Far to unrelated in theory, for them to cross, even though the fruits look somewhat similar.
Cranberry & blueberry are both in the same genus, Vaccinium, so I would anticipate that hybridization *could* be accomplished - though I don't know why anyone would want to.

Cran-Blueberry is one of my favorite juice blends, so I'd have no objection to someone crossing the two species. Maybe the result would be as striking as the Loganberry, which combines the aroma of blackberries with the "tang" of raspberries.

Maybe someone could develop a cranberry that doesn't require bog conditions.

Karl King