Using the Invoices as a model, the businesses available would be your products. A visit records would be the invoices and the specific businesses represented during that visit would be the LineItems.
Just like the invoices starter solution or this simpler demo file created by Comment: http://fmforums.com/forum/showpost.php?post/309136/,
I'd use a drop down menu inside a portal to VisitRecord located on the Visit layout for selecting the businesses represented during that visit.
Or is this a case where all people visited on a given date will all receive information on the same group of businesses and you don't want to enter the same info line item by line item on every visit record?
Thanks! This is what I was looking for!