Hi Luke,
Hosting a server like this is a large undertaking and would need to be done in a coding language other than Game Maker Studio.
Game Maker Studio is great for making client side applications, however, cannot handle more than 1000 TCP connections as a server and would use too many system resources.
I would lean towards creating a server from C# (check out the web for examples), but you will need to learn some intermediate C# programming to be able to accomplish this.
The client would still be made in the Game Maker software, and would use TCP Raw functions to connect and communicate to the C# server.
Finally, Game Maker currently does not support IPv6-only TCP network connections, so in the end, if you are looking to release the game on IOS specifically, Apple will reject your game every time.
Painfully, this is something I learned after spending 2 years developing my game and trying to release on the Apple store. I am trying to work with the GMS staff to resolve this issue, but still in the early stages.
Hope this information helps.