A general rule for the fighting game genre is that grabbing moves ignore blocking or shielding. If you've played Smash or Pokkén, or even any "real" fighting game, you'll know what I'm talking about. So an idea I had is to implement that element in core Pokémon games, making grabs a sub-type of moves with some unique properties like sound-based moves. There are already existing moves that would be changed to function as grabs, such as Vital Throw and Sky Drop.

Now the main property of grabbing moves would be ignoring Protect, Detect, Spiky Shield, Mat Block, King's Shield, and Obstruct, similar to how sound-based moves ignore Substitute. Some other interactions could, for example, be:
>Sticky Hold and Heavy Metal make the user resistant or immune to grab moves
>contact abilities like Poison Point/Flame Body have a 100% chance to activate if the user is grabbed
Plus you could invent a whole range of new abilities and moves around this mechanic, like a Psychic-type attack called Psycho Toss, which has the user lift and throw its foe using telekinesis, or Heavy Lifter, which would boost the user's damage with throw moves (a la Strong Jaw and bite moves), and/or cause it to ignore the resistance granted by Sticky Hold and Heavy Metal.