Yoshi's Island 2 had the nifty idea of having multiple babies, each with their own abilities (Baby Wario had a Magnet that drew in coins, Peach used her Umbrella to glide) when they were on Yoshi's back. Combine this with a power up system based around the food that he eats (with a Kirby Squeak Squad Stomach inventory) so he can have different powers like Sunshine Juice Spit, Bulb/Blimp/Dash from Galaxy 2, Wing/Slam/Fireball from World etc. etc. (exanding on the Watermelons from the first Yoshi's Island, and also having the default Watermelon spit as well)
Eggs are also affected by power ups (Fire Yoshi makes lava eggs that deal persistant damage/melt sufaces/burn enemies, Bulb Yoshi eggs act as placed torches to help light areas ahead) and used as resources for other abilities (Smash style egg shield costs one egg to give Yoshi a stationary shield that will break after a few hits, use all of Yoshi's eggs as one big egg like in Final Boswer to deal more damage, fire and egg downward to double jump like in Klonoa/Ristar).
Equipable Saddles/Shoes to alter behaviors of babies and Yoshi's mobility (Saddles can prevent babies from being knocked off or make them drift differently when bubbled, shoes can stop slipping or allow for bouncing off of spiked enemies like in World etc.)
Have the weird body horror transformations be more like Wooly World where they are more like costumes he wears (so he would dress like a cardboard Submarine, Plane, or Mole to mimic those abilities) so that he can quickly put them on/take them off much quicker and still make use of the babies.
Fully explorable hubworld that leads to all the levels, so you can explore the island and still have proper individual stages. Make the game be similar to Yoshi Story, each world only mandates 1 level to beat but 100% is to go back and complete all the levels, so you can speedrun the game to get to the end if you want but there's still weeks worth of levels your skipping over (but can go back and play whenver you want to get all sorts of goodies like power ups and stuff).
Ironman mode like Yoshi's Story, every Yoshi is a life and there are secret extra Yoshi colours you can find for more lives (Good Guy Shy Guy to save captured Yoshis).
Use tongue like a grapple hook to swing on things like Chameleon Twist, even have that nifty pole vault jump as well (maybe a sticky Yoshi that can drag himself to walls?).
Birdo is Vergil, keeps appearing in rival fights to steal babies (She wants to prove that she's a girl by being a "Good Mom" to all the kids, but doesn't realize she's being tricked by Bowser until the end). Final Boss 1st Phase is Baby Bowser (or whoever) riding on his back, second phase is Mecha Birdo, Third Phase Birdo teams up to face Big Baby Bowser. Becomes playable in Post Game with Infinite Eggs (triple egg jump), can't use Power Ups, no tongue, and will humorously not commit to transformations (finds them gauche, will use magic ring to skip over them because funni).