There are about 20 endings in the School Days Visual Novel. Here's the episode 6 routemap from School Days HQ:
Large image (severe spoilers)
The last leaves of the routemap tree can be duplicate (I know a single case, there can be more). The only reliable information about what ending you get is the title appearing at the end of a route, with the heading "Final Episode".
The attached routemap shows the title of the endings I know as of the time of writing, and the images you get in the main menu as a result of the route (see the two samples embedded in the routemap).
The number increases if you count "double" endings, where Makoto goes out with more than one girl and get a primary and a sort of secondary ending, explaining a particular outcome
In one case, two girls are present in a single ending.
Makoto actually can date girls he doesn't get in the anime. In fact, there are more endings than girls. However, the two main heroines are Sekai and Kotonoha, and even the in-game graphics show Makoto's affection for them in the upper bar: red is Makoto's affection for Sekai, green is Makoto's affection for Kotonoha:
This is the reason why the anime almost only shows these two characters. On the contrary, by meeting particular conditions, you can choose other heroines in the game. Actually, there's even an ending where Makoto cannot get any girl, continuing to live his life normally without any love interest, though it's not included in the episode 6 routemap above.
As far as I know, Nanami Kanroji is and remains a supporting character in both the anime and the game.
However, Nanami's friend Setsuna and her teammate Otome are heroines, as well as Sekai, while only Sekai is an heroine in the anime.
It's understandable, considering that Nanami Kanroji already has a boyfriend. She talks a lot about him to her friends and he appears during the School Festival:
He is an otaku who likes playing visual novels, and he likes to be called oniichan by her when they have a sexual intercourse during the School Festival.
Being in a relationship herself, Nanami is in a good position to judge other characters' relationship. Nanami's role in the game seems to be judging Makoto's actions towards her friend Sekai, she has a very important role at the end of one of the routes. A hypothetical relationship between Makoto and her would destroy her credibility in the eyes of the player, reducing the impact of many key scenes.