Can I apply multiple predicates to an NSFetchRequest? Would it be better to manually parse my results?

Yes it’s possible. You’re looking for compound predicates and here’s an example with AND predicates:

NSPredicate *compoundPredicate 
   = [NSCompoundPredicate andPredicateWithSubpredicates:[NSArray of Predicates]];

You can also use notPredicateWithSubpredicates and orPredicateWithSubpredicates depending on your needs.

Link to documentation https://developer.apple.com/documentation/foundation/nscompoundpredicate