The 'T Method' is the only technique I know of that can reliably determine the advantage of any system.
This video introduces the T Method and steps through using it to find the MA of several systems, before introducing a complex MA system and using the T Method to find its Ideal and Theoretical mechanical advantage.

0:00 Introduction
0:28 Overview of the T Method
1:13 Pulleys & the T Method - IMA
1:48 Pulleys & the T Method - TMA
2:28 Rope Grabs & the T Method
3:28 Example - Simple system
5:05 Example - Compound system
6:50 Complex system - IMA
8:24 Complex system - TMA