Sub-stories and interests can be developed successively or simultaneously or both.
When they’re successive, one sub-story rises and climaxes, to be followed by a second, then a third, and so on. Fantasy probably uses this structure more than any other genre nowadays. The classical quest is a string of adventures as the protagonist(s) move(s) on from place to place.
Simultaneous sub-stories build up at the same time. This is also common in fantasy, where separate strands of sub-story spread out to cover a whole world. I guess fantasy is more diffuse and less centralised than any other genre.
Separate strands can be presented in long blocks at a time, as in Tolkien’s Lord of the Rings. Nowadays, though, the usual technique is cross-cutting between strands. It’s the universal technique of film-making—and it’s one of the changes Peter Jackson makes when turning LOTR into film.
How often to cut across? If it’s important to show how developments are all going on at once, building up together, then very rapid cross-cutting is in order. If you want greater immersion in the sub-stories and lives of the characters, then you’ll probably cut across between, say, chapters rather than sections within chapters.
I seem to slip towards the middle ground between successive and simultaneous. I planned my gothic fantasy, The Black Crusade, as a quest of one adventure after another, but, in the writing, the travellers (Martin Smythe and the mad cultist crusaders) started to develop long-term sub-stories among themselves. Halfway through, I had to go back and rewrite the first part of the novel.
On the other hand, with a more simultaneous structure like Worldshaker, I find myself wanting to bring one sub-story to the fore at a time. Not to the exclusion of other sub-stories, but more strongly presented. There’s always some exciting development in some strand crying out to be given special attention.