No assistance
Belly Drum: +6
Geomancy and power herb: +6
Fillet Away: +6
No Retreat: +5
Clangorous Soul: +5
Shell Smash: +4 (+6 if you ignore the drops or have a white herb)
Simple and any +2 move: +4
Scale Shot: 0 (+5 if you ignore the drops)
Requires some assistance
Simple beam and one of the +6 setups from above: +12
Rattled, weakness policy, and beat up: +10
Water compaction, weakness policy, and water shuriken: +10
Commander: +10
Stamina, weakness policy, and super effective move that hits 5 times: +9
Steam engine, weakness policy, and water shuriken: +9
Anger point, weakness policy, and a guaranteed critical hit move: +8
Justified and beat up: +6 (no Pokemon with justified is weak to dark)
Weakness Policy: +4
Decorate: +4
Memento and contrary: +4
I think these are all the ways to get more than +3 boosts in one turn. Please comment if I missed any
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