I either ignore aspirations completely because I'm too busy with my own storyline, or I switch between a few different aspirations that fit the story I'm playing. For example, I've got a couple sims working on the Strangerville mystery, but I only activate that aspiration while they're actually working on it. At other times they each have a couple different aspirations they can work on at home. And while they were on vacation in Granite Falls, I switched them to the "outdoor enthusiast" aspiration to represent the idea that they were getting away from their ordinary lives while they were on vacation.
I love that we are able to do that in Sims 4. It makes sense to me because most people in real life aren't single-mindedly focused on accomplishing only one thing at a time, so sims changing their goals in different situations, and then coming back around to old goals later, makes them seem more real to me. And, because I play with aging turned off, I like to take a really long time to actually accomplish the aspirations. If I do one aspiration at a time, it gets completed way too quickly.