Alright, so here's something I was thinking about - taking prizes by only playing items. This is one I thought up, with a single field blower - of course, this will never happen in a real game but it's fun to ponder.
To set this up, your opponent needs a Team Plasma Umbreon (above) with a Bodybuilding Dumbbells attached and 13 damage counters on it. Then, the rest of their Pokemon can be Team Plasma EXs, however they must each be 1 damage counter away from a knockout.
Field Blower away the Dumbbells to KO umbreon, which in turn will knock out all of the EXs since they have 20 less HP each. Therefore, you "take 11 prizes" (theoretically of course, unless they've been using Dialga )
The basic premise is right, it is just some things I'd like to mention.
Your opponent's Pokémon all need enough damage counters on them to be nearly KO'd, so it isn't really taking Prizes with just an Item, ya know?
You can do the same thing with Startling Megaphone or Tool Scrapper.
You can do the same scenario with Hypnotoxic Laser provided Umbreon [Plasma] is Active and has just 10 HP left.
You could also have Field Blower discard an HP boosting Stadium like Aspertia City Gym or Training Gym while its boosting all the Pokémon in play. This also means you could have up to 12 Prizes, as you could have six two-Prize Pokémon getting KO'd.
You can play one Item card and take 18 Prizes at once with the following setup. Note: Like yours, I'm not worrying from where the damage counters I'm about to mention came.
Sky Field as the Stadium
Nine 2-Prize Pokémon, each only being kept alive by an HP-boosting Tool, all on one side of the field.
A combintation totally nine of the following: Body Building Dumbbells, Fighting Fury Belt, and Giant Cape.
Theoretically, with the same setup you could have 34 prize cards taken in one turn. I didn't see anywhere mentioning this being a limit to a single player taking prize cards, so assume both active Pokémon are the Team Plasma Umbreon with Body-Building Dumbbells, Sky Field is out as Otaku mentions and each play has 8 Team Plasma Pokémon-EX on their bench that have taken 1 more damage counter than they should normally be able to take thanks to Dark Shade, Field Blower would allow 34 Prize Cards to be taken.
On top of that, I enjoy the idea of a scenario where Dialga & Palkia Legend would be able to actually allow this to happen. Each player could run 3 Beldum, 3 Metaang (or Rare Candy), 3 Metagross-GX and 3 metal energy (as well as a battle compressor, realistically) both could add 17 Prize Cards and trade knock-outs or add 1 prize cards and AZ their Metagross-GX up before dropping down all their Pokémon-EX.
Edit: Just noticed dialga was mentioned in the OP already. RIP.