It is possible to rank for inner pages, but this is usually in the case of Yellow Pages and similarly supplied data to G Maps. A business listing URL in one of these directories can appear in the Place Search SERP. I haven't seen an owner-supplied listing such as your example show up in multiple SERPs. I have never seen an affiliate site in the Place Pages, but this doesn't mean it is not possible to show up there at least once.
PS. Please use example.com and not others such as mysite.com (which is a web hosting company)
What I meant is that you could design your pages to show a local address for each locality where you say you have a business, but these would need to show a different phone number at least; better still, a different address and then one of them might show.
An "affiliate site" can have different meanings. A CPA might have a physical office but also have a page showing some recommended books for customers, which happen to be affiliate links. This will most probably show up as a Place Page. It's all in the fingerprint you show to G.