Draw and Dig

Professor's Research

Another iconic draw Supporter. Combos well with Items that discard as costs (e.g. Ultra Ball, Secret Box); after you've emptied your hand, play Research to fill it back up!

Recovery cards (e.g. Super Rod, Night Stretcher) can mitigate the downside of Professor's Research. Sometimes you'd even want to discard cards, because you have synergies that depend on them in the discard pile (e.g. Gardevoir ex, Ethan's Typhlosion).

Fezandipiti ex

Once setup is over and players start trading KOs, Fezandipiti ex becomes live. Flip the Script draws 3 cards for a fairly easy-to-meet condition at that stage of the game.

Fezandipiti ex is a good counter to being Iono'd to a low hand size. If you topdeck Nest Ball after the Iono, it can turn into Fez.

Note that KOs that occur during Pokémon Checkup (from Poison, Burn, Froslass's Freezing Shroud) don't enable Fez.

Mew ex

Restart doesn't discard or shuffle dead cards from your hand, and it only draws at most 3 cards, but it's an Ability, freeing up your Supporter for the turn.

A common play when you're down to 2 dead cards and an Ultra Ball in hand is to Ultra Ball for Mew ex, granting you a fresh 3. If you already have Mew ex in hand or in play, you can even fail to find, using the Ultra Ball purely as a discard outlet.

Squawkabilly ex

Squawk and Seize's effect is similar to Professor's Research, but draws 1 fewer card.

Often used to set up Energy in the discard pile for acceleration. Like Carmine below, it can be used on your first turn. Nest/Ultra Ball can search for it.

In a pinch, Motivate can also accelerate Energy.

Cleffa

Like Tropical Beach from BW Block, Grasping Draw draws you up to 7 and ends your turn. However, it's an attack, so you can't use it on T1 if you go first.

Your deck needs to be fairly slow to want Cleffa in it. You can't be attacking for damage early (you'll be attacking with Cleffa instead), and you need comeback cards like Iono or Counter Catcher when your opponent takes the "free" Prize from KOing Cleffa.

Carmine

A discard-and-draw Supporter for when you absolutely need one on turn 1, even going first.

Played in low setup decks that benefit from having Energy from the discard pile: Archaludon ex, Roaring Moon (Professor Sada's Vitality), Ceruledge ex.

Tatsugiri

Somewhat similar to Cleffa in that it needs to be Active, can setup for 0 Energy, and gets KOed easily. It has a different payoff, getting a Supporter from the top 6 instead of drawing cards.

In the mid-late game, if you have a way to switch Tatsugiri out (which could be as simple as an Energy to retreat), you can bring it up after a KO, use its Ability for value, then switch it out and resume attacking.

Dudunsparce

For a 2-card and 1-turn (Basic + Stage 1) investment, you get to draw 3 cards.

Commonly played with Artazon. If it isn't bumped, Artazon can be used repeatedly over several turns to get Dunsparce out of the deck after Run Away Draw.

Revavroom

Similar to Delcatty from the EX era, Revavroom is a Stage 1 with an Ability that discards Energy to draw cards. 

Played in Ceruledge ex to dump Energy into the discard pile for Abyssal Flames.

Enriching Energy

If your deck needs 0 Energy to attack (Conkeldurr), or has unlimited Energy attachment (Baxcalibur), you can use Enriching Energy along with Dudunsparce as a draw engine that recycles itself.

Hilda or Colress's Tenacity can search it out.

Morty's Conviction

An option for decks with a 2-card combo where both pieces have to be played at the same time (e.g. Rare Candy + Stage 2). If you've got one combo piece in hand and are looking to draw into the other, Morty's Conviction won't bottom-deck or discard the piece you're already holding, unlike Iono or Professor's Research.

Your opponent will likely have a big Bench if they are on the Noctowl + Area Zero Underdepths engine.

Explorer's Guidance

Provides a minimal amount of card advantage, but also fills up your discard pile.

Roaring Moon makes good use of the incidental discard, as discarded Energy is food for Professor Sada's Vitality, and discarded Ancient cards pump Vengeance Fletching.

Surfer

This is neither a good switch card (actual Switch is an Item) nor a good draw Supporter (other Supporters draw more cards), but helps compress deck slots by being both at once.

Played with Iron Valiant ex, which needs lots of switch effects.