Can an S Corp operate more than one business?

Yes, a S Corp can operate.  In the absense of any other agreement, the profits from the businesses would be distributed based on the percentage ownership in the corporation.

You can have subsidiary corporations in many instances but you would have to check state law.  I could see doing that but the other why would you want to?  I could see if the businesses were in some way related and even then I might  not think it was the best business move to make.  Your state law may even prohibit it.  If it did not then I would think that you would have to keep two sets of books at the very least for accounts paid and accounts receivable.  Are employees going to be employees of both businesses?   Go and seek help from an attorney and/or an accountant to discuss what you want and what works for you.  Good luck.