Frogadier is a fairly capable special attacker, especially with Protean, Life Orb, its decent Special Attack stat and a wide array of powerful special moves, but what holds it back from being truly effective in PU is its poor bulk and its inability to KO faster threats without Paralysis / Sticky Web / Tailwind support. Similarly, it struggles against powerful Pokemon with priority, like Pawniard and Mightyena. However, there's a move it could receive to alleviate its somewhat disappointing Speed stat and improve its ability as a cleaner, without making it too overpowered in PU.
+ Vacuum Wave
Justification: It wouldn't be inconceivable for the Greninja line to receive Vacuum Wave through breeding at some point, given its froggy brethren, Toxicroak and Croagunk, already have access to it. By simply adding Froakie, Frogadier and Greninja to the Humanshape Egg Group, this could become possible. According to its Pokedex entry, "It appears and vanishes with a ninja's grace. It toys with its enemies using swift movements, while slicing them with throwing stars of sharpest water." With Vacuum Wave being quick and Ninja-like, this move would suit Frogadier aesthetically, too.
Theorymon: The problem with justifying a team slot for Frogadier basically boils down to the fact that other offensive Water types in PU often make it so it's left behind in favor of more viable options, like Poliwrath or Floatzel. Floatzel is at a superior speed tier and has slightly better bulk, while Poliwrath is much more splashable and provides teams with a multitude of resistances and an immunity to Water type attacks.
However, with the addition of Vacuum Wave, Frogadier would need less support and could fit in on most offensive teams (especially on teams where a cleaner is needed, like on Spike Stack). Frogadier could also see some use over Poliwrath, as it receives STAB from every move it gets, it hits harder, and is much faster (save for Poliwrath's offensive RD sets).
Vacuum Wave Frogadier would still be a step shy from being overpowered because fast Psychic types who resist Vacuum Wave still exist, like Scarf Mr. Mime and Kadabra; they would be able to take a hit and KO back with STAB. Similarly, Special Walls like Regice and Lickilicky would still be able to sponge a hit from Frogadier, even with this new super effective coverage. Vacuum Wave would simply make Frogadier better in terms of its cleaning ability, and against Pokemon with priorty, like Mightyena and Pawniard especially.
Here's what a possible set would look like:
Frogadier @ Life Orb
Ability: Protean
EVs: 252 SpA / 4 SpD / 252 Spe
Timid Nature
IVs: 0 Atk
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Vacuum Wave
- Grass Knot
- Hydro Pump
- Ice Beam