As of Legends: Arceus...
Pokemon that have more than three abilities, ones with italics are ONLY in previous generations:
1. Basculin - Reckless (Red-Striped and Blue-Striped), Rock Head (Blue-Striped), Rattled (White-Striped), Adaptability, and Mold Breaker
2. The Chandelure Line - Flash Fire, Flame Body, Infiltrator, and Shadow Tag
3. Indeedee - Inner Focus (Male), Own Tempo (Female), Synchronize, and Psychic Surge
4. Meowstic - Keen Eye, Infiltrator, Prankster (Male), and Competitive (Female)
5. Rockruff - Keen Eye, Vital Spirit, Steadfast, and Own Tempo
6. The Scolipede Line - Poison Point, Swarm, Speed Boost, and Quick Feet
7. Toxtricity - Punk Rock, Plus (Low Key), Minus (Amped), and Technician
Pokemon that have 4 abilities due to their mega form, these are Pokemon with two regular abilities, one HA, and have a 4th gotten through mega evolution that's different from the rest of the abilities, or the Pokemon has two megas with different abilities, and two abilities from its base form. The abilities in bold are the ones gotten through mega evolution:
1. Absol - Pressure, Super Luck, Justified, and Magic Bounce
2. Aerodactyl - Rock Head, Pressure, Unnerve, and Tough Claws
3. Aggron - Sturdy, Rock Head, Heavy Metal, and Filter
4. Alakazam - Synchronize, Inner Focus, Magic Guard, and Trace
5. Banette - Insomnia, Frisk, Cursed Body, and Prankster
6. Camerupt - Magma Armor, Solid Rock, Anger Point, and Sheer Force
7. Charizard - Blaze, Solar Power, Tough Claws, and Drought
8. Gardevoir - Synchronize, Trace, Telepathy, and Pixilate
9. Heracross - Swarm, Guts, Moxie, and Skill Link
10. Houndoom - Early Bird, Flash Fire, Unnerve, and Solar Power
11. Kangaskhan - Early Bird, Scrappy, Inner Focus, and Parental Bond
12. Lopunny - Cute Charm, Klutz, Limber, and Scrappy
13. Lucario - Steadfast, Inner Focus, Justified, and Adaptability
14. Manectric - Static, Lightning Rod, Minus, and Intimidate
15. Mawile - Hyper Cutter, Intimidate, Sheer Force, and Huge Power
16. Mewtwo - Pressure, Unnerve, Steadfast, and Insomnia
17. Pidgeot - Keen Eye, Tangled Feet, Big Pecks, and No Guard
18. Pinsir - Hyper Cutter, Mold Breaker, Moxie, and Aerilate
19. Sableye - Keen Eye, Stall, Prankster, and Magic Bounce
20. Steelix - Rock Head, Sturdy, Sheer Force, and Sand Force
Note: This excludes Alolan and Galarian forms, as 90% of the forms would be apart of the list.
Source: Shuffling through the Pokedex seeing if any Pokemon has more than 3 abilities