So if a site gets three pages ranking on the first page, they're all going to go one-after-another in the search results?
Yes or No.
If Google decides to show all three pages they will all appear on the first page of the search results. However, Google, in my opinion, has a domain diversity goal and does not show all of the pages from a single domain in many situations. Those pages that are not shown go into what many people call the "supplemental results". You can see the supplemental results if you search to the end of Google and find their words....
"In order to show you the most relevant results, we have omitted some entries very similar to the 140 already displayed.If you like, you can repeat the search with the omitted results included. "
So, it is possible for you to earn three positions on the first page of google and only get one or two.
These "double" and "triple" listings can be very valuable because they push your competitor down the page. They are very difficult, almost impossible to get in extremely competitive SERPs. However, they are much easier to get in less competitive niches and can be worth going after. I go after them a lot. If I have a retail page and an article about the products, I often get positions 1 and 2 from that combination. If I have several extremely different articles about a topic, I frequently get 2 or 3, or even 4 pages at the top of Google.
To achieve these you need a site that is one of the strongest in its niche and a site that has a prolific author who can produce more than one page that will rank well for the keywords that you are targeting. I don't think that keyword cannibalization is a bad word because I've made a lot of money from it.