For example: I have a Lightroom catalog for business photography and a Lightroom catalog for family - occasionally I will have photos that belong in both categories, I would like to have the originals accessible by both catalogs with changes made in either catalog synchronised to the other.
I am using LR 5.6
Sure you can... however you would be best to have just one catalog as it is tricky keeping files in more than one catalog in sync and knowing what changes have been made where and when.
Try using different Collections for business and family. I have over 500k files in one catalog....I use collections for clients and other needs.
Yes, that might be a better option - tidy and simple!