In the end, my ideal format is actually just Modern with the more interesting and unique Legacy cards added in. One way to do that is with a heavy-handed treatment of the Legacy Banned list. The other way is to either open up the Commander sets for Modern (while banning key cards like Sol Ring), or to make Modern-specific printings (like Modern duel decks). This would add a lot to the format without breaking Standard.
Off the top of my head, here’s a set of cards that could make Modern deeper and more interesting:
Baleful Strix is absurd in the right matchup, especially against people trying to tempo you out with a giant creature, but it doesn’t solve control’s main problem in Modern: The inability to apply pressure when necessary.
Strix is one of the best cards for recovering from mulligans, and it’s one of the more satisfying value creatures in Magic.
Cabal Therapy is one of the greatest skill-testers of all time, and it makes for a ton of great stories. When it was legal, it almost singlehandedly made Extended my favorite format.
Misdirection is a unique and interesting one. While it’s fairly risk-free, and would introduce some complicated and confusing situations to Modern, it wouldn’t actually solve any of Modern’s problems.
Goblin Lackey is far from enough to make Goblins tier 1, especially since we’d still be missing Matron and Ringleader. However, it would give Goblins another explosive opening and possibly push it into the realm of viability.
Council’s Judgment is expensive enough that it wouldn’t overrun the format, but unique and powerful enough that it would influence things. Council’s Judgment is definitely a tool that I’ve wished for in the past.
As with Council’s Judgment, this is more about introducing a new tool into Modern.
Modern mana bases ensure that your life total is usually way lower than it is in Legacy, which is why there are many more Snapcaster + Lightning Bolt decks and also why Burn is a more successful deck. Since Toxic Deluge uses that resource, it’s even more balanced and interesting than it is in Legacy.
Grenzo, Dungeon Warden, Edric, Spymaster of Trest, Dack Fayden
These are all interesting, powerful-but-not-overpowered cards, and they make people excited to play Magic.
Aluren doesn’t even have the cards to combo effectively in Modern, but it’s still interesting. It requires a high creature count to abuse, and it’d be interesting to see if anyone did anything with it.
Force of Will
The only way it works is if it’s not actually overpowering. In Legacy, some lists only run 3 Force of Wills in the main and cut it completely in the grindier matchups. If Force turned out to be a real liability in some spots (Dispel is already one of the better counters in the format), then it’s possible that it could provide a much needed generic answer for the various combo and engine-based decks without making a mess of things, effectively taking on the same “glue that holds the format together” role that it does in Legacy.
Decks that would get a boost, like Twin and Merfolk, are also decks that lack dedicated draw. Merfolk in particular lacks a way to recoup card advantage.
Failing a Force of Will reprint, actual Counterspell could do work. The problem currently is that decks don’t have an answer to both Primeval Titan and Hive Mind, or Karn and Wurmcoil Engine that isn’t too slow or too narrow.