I think that really depends on how much continued success it has, how long Grey's Anatomy keeps running, and whether or not they plan on continuing after Grey's ends.
Station 19 could end before or after Grey's (although they've made before harder with marina's marriage). If they throw in another crossover couple I'll be inclined to lean towards after, because it'll be a way to keep GSM alive if, say, Jack and Jo start dating too.
It really depends on behind the scenes decisions, though. I have no real clue. It could turn into the next Grey's, and thirteen years from now we're watching Maya get sassed by her pre-teen .
Unless the ratings take a major hit, then I think this will go on a few more seasons. With Grey's coming to an end soon (either next season or the following), they'll probably use this show to keep the Grey's universe going (and add another spinoff). If they cancel this show along when Grey's ends, that's the end of Shondaland on ABC and considering they are their top rated shows, it would be crazy to let that go.
Unlike the other Shondaland shows (Grey's, PP, Scandal, HTGAWM), this show doesn't have a character that they absolutely need to keep the show going. Andy may technically be the lead, but if she left, the show would be just fine and it can focus on the station and the other characters. They proved that by moving Andy to 23 and Station 19 is just fine without her there. Any of the characters can leave and the show can keep going (whether that will affect quality is another topic).
Considering ABC is holding on to Grey's for dear life, they'll probably keep S19 to 10 seasons. Or until they get another hit show or two.
