Can you be specific of what you need to morph? With Characters you can get away with a lot, using the same topology -
If it’s something like going from a screwdriver to a dinosaur (that’s an actual example I’ve seen in production 
) it might be a tad trickier. As for the morph order, that doesn’t matter that much, you can use driven inbetweens, corrective shapes, whatever is needed. Always depends on the task.
(The gif above was created using the mesh fairing addon)