Multiple Delegates in iOS
I've worked on projects where people have attempted to use multiple delegates and it's basically a bad idea. The delegate pattern is about a 1 to 1 relationship between a class and it's delegate. Whilst it is possible to achieve some level of multiple delegation through switching the delegates in and out, it's more likely to lead to unpredictable behaviour and bugs.
My recommendation would be to change how you are thinking about this. You have two options as I see it:
Switch to an Observer pattern where you can register multiple observers which your main class can interact with. This is useful where your observers all implement the same protocol and where your main class wants to be aware of the observers and interaction with them.
Broadcast NSNotifications to indicate state changes and events. Here is a more decoupled approach because the main class does not need to know who is listening and does not directly interact with them. Other can start and stop being notified at their leisure. It also has the advantage that you do not need to create or implement a separate protocol. Instead you register the classes that need to know about changes with the NSNotificationCenter which in turns handles all the routing of notifications for you.
It actually sounds like the delegate pattern might not be the best approach here.
I would look into NSNotificationCenter instead.
The basic idea is that your singleton doing the net connection posts a notification (with something like postNotificationName:object:userInfo:) , saying that new data is available. Within this notification, you can pass a dictionary object (userInfo) that holds the data you've fetched, or info on what parts of your Model contain updated data.
Then, your other view controllers can register themselves to 'observe' these notifications by calling addObserver:selector:name:object:. Generally speaking, when a vc becomes visible I call addObserver, and removeObserver when it's being hidden or transitioned out.
Good luck!