Im running through just about every combo I can throw at each frame right now, and the WS it uses seems to be based on an average of whatever elements you have on it (possibly related to burden). It seems that SE has found a way to make PUP veer away from the old combos of FM FM FM/TM spam and actually improving the overall performance of the puppet. This also makes Overdrive actually worth it now (although it needs to last more than 30s) by making 1 maneuver = 3.
It will Cannibal Blade @ full hp if no maneuvers are up, it will also Cannibal Blade with Earth/Wind/Light/Dark stacked up to 3x each. A single Fire maneuver will force Chimera Ripper and a single Thunder maneuver will trigger String Clipper, so if you're fire loaded you get chimera / thunder loaded you get string (this is actually the opposite of what it used to be, 3x FM spam would always use String Clipper). Dark seems like the overwriting maneuver for Cannibal Blade, but it will not overwrite 2 opposing maneuvers (2 FMs 1 DM and it still uses Chimera, etc.) Granted this is all initial testing and Im sure there will be some outlying examples / maneuvers wearing off mid test/ etc. so this isn't conclusive (yet).
Daze functions the same way, but its only limited by one other possible WS so you only have to consider FMs. A single FM, or being "Fire loaded" will force Arcuballista, anything else and it will use Daze. We lucked out on Daze because it seems that Thunder acts as an overwriting maneuver, so you can FM/TM/LM (or WM) and it will still use Daze. What needs to be figured out now for each person is what WS you want and what other effects you want to maintain (flash, erase, etc.) while maximizing maneuver effects. I actually like what they did with this (short of not being able to FM FM FM + Daze) because it keeps performance up while minimizing overload and allowing you to utilize more of the puppet's abilities without sacrificing dmg.
Edit : initial testing also seems to have Wind as the overwriting element for Knockout (Thunder loaded = Slapstick, TM + FM = Slapstick but TM + FM + WM = Knockout, etc.) Knockout is also the only one I've been able to trigger with multiple FMs.