Historically the path of optimization to the point of breaking the game lies in a few different areas.
- Multiclass level dipping
- Spells and spell combinations
- Action economy, extra attacks and action surge like abilities, bonus actions
So far it seems like the greatest benefit of multiclassing is to help with the other two categories. So taking a couple levels of fighter for action surge, or a couple levels of rogue for cunning action, or mixing spellcasting classes for spell diversity, seem like your best bets.
I think the bard class with it's magical secrets ability will be the center of some very good game breaking combinations especially as more and more spells are released, bard might just be the top tier casting class at higher levels.
But my best advice to game the system and optimize is know your DM. Just like in poker don't just play the game play the person, so look at house rules for exploits, play his pet race, if he uses fumble rules play a halfling, stuff like that.
I love theory crafting and optimization and hope we can get this back on track, I have been breaking the game and having fun with it since 1st edition with my dart throwing weapon specialist fighters, and in 2nd edition with my bladesinger kit elves, always looking for the best exploits.