Here's what I'd do for a Star Fox game:
Command would be retconned, and the game would take place after Assault A movie quality story, and branching dialouge like Mass Effect or Fallout 4, also explaining character backstories more, Space combat levels have been taken off rails, aka All Range Mode,Upgradable weapons and craft A slightly edgier storyline New enemies Different story options (I.e Fox's story, Falco's story, Krystal's story, Star Wolf, etc.) that show the story from another character's perspective and telling their origin stories, they are unlocked after beating the previous story Some team based elements On foot combat returns, but is slightly slower paced, you can switch between 1st and 3rd person views, oh and you can now aim with all weapons (AKA all weapons have iron sights) Online multiplayer with Voice Chat Local Multiplayer
Hidden Lore about Lylat is discoverable based on missions
Team Based Gameplay
Also the story is supposed to be slightly more serious then past games, also gone is the Cheesy dialogue and bad voice acting of past games, replaced with serious dialouge with some humor thrown in. Also gone is the old puppet visuals, replaced with realistic characters.
The different stories also provide backstory
(Fyi: By serious, I mean less campy, not an ultra realistic story which is too serious, think like Star Wars)
The Great Fox (or Sargasso) would serve as an interactive hub world in between missions, with different characters that provide a useful purpose, (Krystal would use her telepathic abilites to provide intel, Slippy would upgrade weapons and vehicles and develop new vehicles and weapons).
Let me know if any of these are good