Profiles can basically be a directory. Each profile being a business. You'd use userlists to search the users (the directory). Otherwise I suppose GJ could be used as a directory where each GJ category is a industry and groups are businesses. The alternative is an actual directory extension for Joomla.

See the below for details about GJ.

www.joomlapolis.com/addons/cb-groupjive

You can also demo GJ below.

demo.cbdemosites.com/addons/cb-groupjive/all-categories

You need to check the Joomla Extension Directory for directory extensions and compare them for your self. Most common one used when I used them was MosTree, but there's likely a lot more available now.

Thanks for the pointers to GJ. It sounds good. Unfortunately I don't think I have enough experience with the tools to compare them for myself.

Feel free to use our demo as much as you like. It automatically resets and is mostly unrestricted so feel free to change whatever you like.

Can you recommend some experts or consultants who can help us make these kinds of choices? We are prepared to pay for the consulting time.

Sorry, I've no recommendations at this time. My guess is you'll need a true directory extension though if you intend to use profiles in addition to having a directory otherwise a profile based directory should work perfectly. GJ supports 1 level of categories with 1 level of groups in those categories so you won't be able to do Category > Sub-Category > Group with it as you mentioned needing sub-categories.